I've currently finished two years of undergraduate study in physics. I'm at the end of a close to two month summer research program in math, at one of the best universities in my country. While I'd applied for a mathematical physics type project, the problem I was assigned has to do more with math and my job is to make a program in order to understand (the outcome of) this problem. My background in mathematics is not good, since the way it works where I study is that there is an extremely small math component in a physics degree and some extremely important concepts in math were excluded from this math component. While I have been studying independently, my course is generally lacking in rigour and depth in coursework so there always ends up being a lot of independent study that I need to do.
I wish to apply for a Master's program in Physics once I complete my undergrad (I'm doing a three year degree) and I'm considering applying to places in the UK and/or Europe. My background in math and my never having had formal education in CS certainly put me at a disadvantage during this internship. However, I am unable to decide if I should be asking this professor for a letter of recommendation in case my applications require one from a summer research guide or someone in such a position.
This is the only such research internship that I will be doing before applications begin (which happen in 2 months) so I do not have the option of asking anyone else for this specific position.
I'm also not sure how having only one summer research experience, and that too not in physics, plays out while I apply for a Master's in physics.
I'm also quite disillusioned at this point regarding just going forward with physics itself because it seems like I already have heaps and heaps of catching up to do and I'm feeling extremely overwhelmed and unsure of whether this is something that I'm good enough to do. I've always wanted to do physics and I enjoy learning and I understand that this is simply one summer, but I am quite anxious at this point.
I'm unsure of what to do, specifically regarding the recommendation. Any help would be greatly appreciated. Thanks.