I am currently a Physics Major looking to transfer from Penn State to UF. I am an honors student here on campus and I do undergraduate research in quantum transport. My first two semesters were a bit rough. The first semester my father was going through a stem cell transplant, and his health was a bit hit and miss. The second semester I was diagnosed with an aneurysmal thoracic aorta. I missed several of my labs which resulted in me getting a C+ and B in the two semesters respectively. I am however, a tutor in Spanish, Physics, Chemistry, and Calculus, and all of the professors on campus can vouch for academic diligence. All of this being said, my overall GPA right now is a 3.0. Should rise to a ~3.2 after this semester. Do I stand a chance at getting admitted as a transfer? I wanted to send letters of recommendation but no one seems to want them! Not sure what to do.
Why do you want to transfer to the University of Florida ?
I am my father’s caregiver and he needs to move to Florida for health reasons. The climate down there is more agreeable to his health. I love Penn State and would most definitely stay if I could. But I also am still a florida resident so in state tuition at UF is very appealing. Also some of the professors there at UF are doing the same sort of research as my UG research.
https://www.advising.ufl.edu/admissions/transfer-admissions/
If you meet the transfer requirements, Physics isn’t a limited access or super competitive major for a transfer student, your chances are fairly good. 
UF doesn’t use letters of recommendations for admissions. However, I would recommend reaching out to the Undergraduate Coordinator, Katia Matcheva. You can explain your situation, and get many of your questions answered.
http://www.phys.ufl.edu/faculty/matcheva.shtml
As a transfers student, the “University” admissions will simply make sure you meet all of the basic requirements for a transfer student, and then they transfer your application to the college. The physics department will be the ones making the final decision.
After you get accepted (hopefully!) reach out to the professors doing research in your field, and ask the meet with them, possibly during office hours. At that point, letters of recommendations around your current research may be useful.
Good Luck!
Only thing I am worried about is in Physics 1, which for us was Mechanics, I got a C+ because of my labs I had to miss. I am hoping they will look at the whole picture and not rule me out completely because of one C+.
They wouldn’t rule you out for one C+. Transfer admissions is based on what classes you’ve taken and what grades you have earned both overall and in the prerequisite classes. If you are denied, there is an appeal process that can take other factors into account to help make their decisions.