Saoirse, I was also not a 1st Gen student when I went to college in the dark ages. And I also had confusion and misgivings about visiting my professors and advisors. This may be something that happens to 1st Gen students, but I think it can happen to any student.
I think your doubts and questions about the situation is a normal thing for some students. Please don’t feel you’re odd for wondering if such a visit is okay. Some students won’t think twice about it – other students will think about it 100 times before visiting or not visiting. Everyone is different.
Now that you know it is okay, please visit the professor. And continue to visit if the professor gives you good advice. If the professor thinks you should consult with someone else, the professor will tell you. Until then, visit the professor.
Good luck at your new school!