Feeling insecure about my relationship, self doubts. Idk how to even feel

I’m a 20M and my girlfriend is 19F—we’ve been best friends since childhood and only started dating about two years ago. We’ve always been there for each other, supporting one another through school, family stuff, you name it. We also were matchmakers for our previous exes. Honestly, I never thought we’d fall in love, but well here we are.

The thing is, she’s so much more mature than I am. She’s been pushing me to study harder because I’m trying to get into an MD program, to wrap up my dream to become a full fledged doctor, and she’s been helping me with subjects I’m weak in, as well as offering emotional support. On dates, whenever she makes more from her internship, she insists on paying because she thinks I’m “wasting money” if I try to split. I get embarrassed about it. I always try to pay and then she gets mad and annoyed at me.. and starts giving me a lecture on the need to save. But yes, for most parts we do split as I told her it feels weird.

My friends also constantly joke that I’m “the girl” in our relationship, and they tease me for being the less successful partner. Also when we hang out it's usually me who does the cooking.. and because of that reason one of by ex-friends belittled me for that. I'm no longer friends with him. I don’t really mind the jokes, but it’s made me start questioning whether I deserve her. She’s beautiful and confident, and I just feel average in comparison. I don't even know if I'm fit for her? Or if I'm worthy to be with such a person like her...

Lately, she told me that once I get into grad school we should get engaged—she doesn’t want to wait until I finish my MD. She’s already locked into a prestigious internship with a guaranteed job afterward, so she’s said that she is fine supporting us in the early days as I wrap up medical school. But the idea of marriage right now throws me for a loop. I had planned to focus on getting through school before even considering marriage, and I’m nowhere close to feeling ready. She thinks it’s better to tie the knot before we turn 25, but between my insecurities and my desire to finish my education first, I don’t know how to respond.

All of these lately have been making me question our relationship. Don't get me wrong... she is an angel and the sweeetest girl I have ever talked to. I love her dearly but all these makes me go into self doubts. I'm very immature.. I can get a lot emotional. I cry a lot after watching a freaking Disney movie... and she is like polar opposite. She is younger than me but so much more mature.

That's also why I really sometimes feel that I'm gonna drag her down unfortunately. A girl like her doesn't deserve a person like me