Disclaimer: I am not a man, but there’s nothing I don’t know about fear of commitment issues.
First off, I think you should accept that your being sad and lonely pre-girlfriend has nothing to do with not having a girlfriend, and if you thought it was, it was just a projection. You sound as if you have been focussing all your dissatisfaction on the fact that if you had a girlfriend, your life would be perfect and you’d be happy, which hasn’t happened.
The beginning of a relationship is always stressful after that first “I’m madly in love! Let’s spend every minute of the day together! Every day!” feeling wears off, particularly for people who are used to spending a lot of time on their own. I’ve learnt that you just have to work through it, and dilute the intensity a bit. Some people need more time alone than others, and if you are feeling suffocated, you need to carve out a little space for yourself. But don’t throw something away now, after a month, that you may regret later. Maybe you are happier on your own, but give it a little more time.
The other thing to consider is that presumably your girlfriend’s feelings are engaged also: the message you are giving to her if you bail out now is that the fun of the chase was great, but you can’t really be bothered now: you made her think she was worth it, but actually, she’s not.
There is an unspoken assumption in new relationships that you have to be deliriously happy to spend your entire time together. Why is it that if you tell your friends you can’t be bothered to go out and want to stay at home in front of the TV, they can think that you are annoying and boring, but not feel that it reflects in any way on them personally, but that doesn’t work in relationships? (this could easily turn into a mini-rant all of its own).
When you’ve been used to wallowing in your own thoughts and/or misery for a long time, it can be really hard to adjust to taking someone else’s feelings into consideration all the time. Be patient, don’t put too many expectations on this relationship, and wait to see if things work out before you take any drastic steps.