Bro, I couldn't believe it when I saw the title of this post.... why? Because I am also a 27-year-old Engineer considering career change to Psychology!
Firstly, thanks to all the people that have replied. You have all put your greatest wisdom and effort into your responses, and I hope they helped Kamill as much as they helped me.
My situation is very similar: I have been graduated 5 years, but I studied Electrical Engineering and now work in Substation Design. So standard: great salary, job security, professional recognition... all great things to be thankful for. A great job all round. The one difference for me is that I struggle with my job, it takes up all of my energy and my boss is a completely non-empathetic perfectionist (definitely not an INFJ!). So I have reason to move job/company/career anyway.
But I feel the same as you... something missing, something not quite right. Some of my fellow Engineers are definitely meant to be Engineers. They care so much about... things! Equipment, boxes, wires! They turn them on, so to speak

Not me though. I like the equations and numbers, but what I've noticed myself gravitating towards at work without any real reason is helping people. When I did the Myers-Briggs test and read the INFJ profile I had the same experience as you; it was like someone had been following me for years and recorded all my deepest drives and logged all my frustrations in the workplace.
Something's missing. Us INFJ's need to be satisfied on a deeper level. Now, I'm usually pretty terrible at realism and common sense (which begs the question why I'm in Engineering), but for this particular predicament of ours I think I have thought things out pretty sensibly:
What is a job? It's something that we spend most of our waking hours doing, from which we hope to get various things. Are you familiar with Maslow's hierarchy of needs? In ancient times we spent our days hunting and gathering, looking for shelter, then chilling and painting caves. This provided our needs of food, warmth, shelter and finally FULFILLMENT, this last one being met only after the first ones.
Nowadays, our jobs have the same role as this activity. We trade our time/effort for money and fulfillment. The money buys us the food and shelter we need, and entertainment too.
I'm sure some of the same thoughts have crossed our minds: Shouldn't I be happy with such a good job? Wouldn't a poor person from India or Ethiopia kill for this job?
If, like me, you live in the developed world then you are in a very privileged position of having the luxury to think about these things. People in poor countries have to work from the moment they wake up until bedtime just to eat. Luckily, that's not our situation.
So, the way I see it is, like someone above said: if you don't have any responsibilities (children, parents to support) other than yourself, then what use of your time and effort is going to provide you with the BEST overall happiness? Consider indeed whether you need to be working at a sufficient professional level in order to be happy (in yourself, not for your parents or peers). Consider also whether having limited money would cause you to be unhappy, and to what degree.
But consider also, that despite the professional level and salary of your current job, it is NOT making you happy. Phoning in sick because your not spending your time in a meaningful way is not happiness. If you had people to support, then not having enough money would indeed cause MORE unhappiness than this due to stress. But that's not your situation.
Can you see yourself doing your current job for the rest of your life? Scratch that, life is long and people change. Can you see yourself doing it for the next 3 years? How does the thought of doing it for the next 3 years make you feel? I'm guessing not happy, not inspired, and not potentially fulfilled.
So the question is, what use of your time provides you with the best overall balance of happiness. Fulfillment, and enough money for what you need right now.
There are only 2 things that you definitely SHOULDN'T do. Number 1 is make hasty changes and end up in a worse position, in another job which doesn't fulfill you, but also doesn't pay well and is less secure. That's just pointless! Number 2 is 'nothing', i.e. don't do nothing and stay in the same predicament for years.
Luckily for you (and me) there are 3 virtually risk-free paths of investigation to go down. Number 1 is to start doing new things in your spare time that are similar to your potential new career. Volunteer for a crisis helpline, do a weekend course in Counselling and/or Psychotherapy, volunteer for non-profit organisations.
Number 2 is an extension of number 1, if number 1 goes well. Can you get away with doing a straight 40 hour week as an Engineer with no emotional investment? Or even less, part-time? And start devoting more of your energy to these "alternative" options? Then you'd get the security of Engineering, with the fulfillment of the other options.
Number 3... if your home country is anything like the UK, then they are desperate for Engineers. Do you really think that if you took 3 years out to explore other options, then changed your mind, that you wouldn't get re-hired as an Engineer? Get your finances and plans in order, and try a series of other jobs for a few years to see how you fare. If you don't like the other options as much as you thought, then you back to programming-land!
My point is, there are intermediate options that allow you to try before you buy. And you might be able to find a more unusual Engineering job/role that lets you help people more directly.
There are plenty of people in shitty jobs who are unhappy, and there are plenty of people who are in good jobs who are unhappy. You don't want to be either of those - life is too short.
There are lots of psychology graduates and not many jobs. But if your capable enough to be an Engineer, and you got behind Psych 100% there's no reason to think you wouldn't be one of the few successful ones.
Also, like someone said above, being INFJ's may mean we need to set up our own environment's that we are in control of to be happy. Like this guy:
Only you can make the decision in the end. But follow the best advice from above:
1. Be sensible. Try before you buy.
2. Listen to your heart/gut. DO NOT ignore how you feel about your current job.
3. Remember that if all else fails, you can go back to Engineering.
4. Think about how you'd feel if you never explored other options. (Hint: bad!)
http://www.rophydoes.com/images/memes/gift_giving/office_01.jpg
PS - I was off work last year for 6 months with Obsessive Compulsive Disorder and depression. I cured myself with the help of a psychologist/therapist. I now post tips on OCD forums to help people recover. When people reply and say that my post has changed their life, it gives me more satisfaction than anything I do in Engineering. Because I know that my effort and expertise has changed someone's life in a huge way. The only question for me is whether I continue to do this in my spare time, or can do it as a career.
Peace bro!
x