I think you should give it a shot!!
I wanted to be a child psychologist and ALMOST finished my degree before I had my daughter. I loved, loved, loved it. Like I couldn't wait to go to my psych classes, lol. But for me, I've learned that it is better as a hobby-learning psychology that is. And I can use it when I work with kids, or even adults for that matter, but its not the right job for me, at least not right now.
And I don't think having a big heart is a bad thing! I am the same way, which is why I decided not to do what I originally wanted to do, which was a social worker, because most of the time in that field you aren't working with people who WANT help. And sometimes, you just can't do anything with all the laws and stuff. But with psychology, they are coming to you, so they, or at least part of them, wants the help, and being there trying to help them with a big heart and compassion is just what they need. All you need to learn is where to put boundaries.
I think you would do amazing!
And my family didn't really understand. They didn't get why I would go to school so long and spend all that money "just" to do psychology...but it was my passion and I didn't care. So I say if thats what you feel is right, then go for it!!