I would if it would help, too. I think for me it might. I just don't know if I have the brain for it.
I get flustered when things get complex, when there are a lot of steps or a lot of moving parts.
I'm surprised about the physics/math/IT people being lost and lonely though.
Here, if you fit in to those groups, you're pretty much on your way. If you're an engineer here, it's like the world is your oyster.
I think you have the brain for it, just go step by step. I thinkg everybody typical(without some mental illness influencing the intelligence) can do it on some level.
How do you think engineering will help you? Let's say you know math, how would it help to fit the world?
Knowing a bayes' theoreme doesn't give you an idea how to live in a real world.
Maybe on the contrary, people can think, you are weird.
I'm a half IT, I can't find a good job, I spend 8h/day pressing the keys and hate it, but there is nothing else I can do. And it's not healthy sitting for so long. I can learn some math and go to the statistics, for example, but it won't change a lot my life.
I know at least other 2 IT persons who works and gets salary 2-3 times less than an average, not becuase they are stupid, they are not, but because they can't manage such the things(getting a new job, asking for better salary, etc). I know even more who can't find a relationship. Not only me, but some of them hate calling on phone(so yes, we mostly write)), afraid of talking to people in the streets, afraid of people. And maybe among IT people(maybe others from your list are the same) there are even more introverts than in general, because you don't need to interact with people a lot, that's why we've chosen it.
Once I was trying to build a simple math model of a friend, I downloaded my friends' and their friends'data from the social nets, and tried to do smth with it. I also tried to do the same with the penpals sites. It was a nice data, but what could I do with it? Trying to write to someone, smth like "look, you have a nice profile and it fits my model..."? It would be stupid and scarry, I didn't. So it didn't work out