I'm going to tell my girlfriend that I don't need help at the gym
Why don't you want to ask for help?
I will lose my confidence if I asked for help and then I might not be able to reach my fitness goals
It is not bad to need help but it is okay if you don't want to ask for it.  Try to challenge yourself and succeed on your own, and you can always ask for assistance if need be.
I still think it would be embarrassing.
Your determination is admirable, and I'm sure that your girlfriend was just trying to be nice, even if it seemed a bit pushy.  It's good to push yourself to meet your goals, but in a work-out context, sometimes it is safer to get help, for example, with a bench-press.  Even someone with much less muscle than you can provide help in a pinch.