Grandy is spot on, nobody is perfect, particularly in relationships, and even the idea that you may have done a particular thing wrong can be a mistaken belief on your part.
Grandy is also right that the peron you are is what attracted your girlfriend to you. This is who you actually are, not who you aspire to be though a haze of self-criticism and doubt. As you mentioned she has tried relationships with other people before, and has found you to compare favorably with them -a compliment which you need to believe -which is why she is with you.
The need to apologize for perceived faults does not really help, it is a sort of reflex action based on the idea that what you did was not up to expectations - mostly yours. You girlfriend might smooth over things and make you feel better short-term, but in the long term if this is always required having to do this places a burden on both of you.
When you think about it I'd expect you would realise it is a lack of confidence in yourself, coupled with anxiety. After all a first relationship can be a worrying time anyway.
So what to do?
May I suggest you need support, both in relationships, but also study too. Trying to fix yourself often does not work, as I found out. I had, amongst other things, anxiety and low self esteem and I only started to improve with the correct medical help -plus family support.
When you last spoke you mentioned you were planning to talk things over with your mum, can I ask how that went?
There is one other thing to remember, and that is your girlfriend will have faults too, she is human after all, even if you think she is perfect (which is only natural). A good relationship does not expect perfection, and makes allowances for the other person . Affection, enjoyment and constancy are important, not perfection
If you would like to talk with a live voice or use chat on-line I'd suggest the professionals at the Kids Help Line (1800 55 1800) would be ideal.
Please say how you are going