Will my Mental health become an issue? Watch
The short version, is no it almost certainly* won't be a problem. Medical schools much prefer applicants and students who have recognised their difficulties, sought appropriate help, and got better, than people who are too scared to get help."Got better" also doesn't have to mean "cured and off medicine / not having talking therapy" - but stable, which for many people will still include regular medicine or therapy.
The ONLY reason I say "almost certainly" rather than "definitely fine" is that obviously for a small number of people - usually with severe and enduring mental illness, occupational health may decide that medicine is not the right thing - either for a short time or in the long term. But these people are few, and it doesn't remotely sound like you'd be one of them if you've not got as far as going to the GP yet.
Admissions tutors will NOT be aware of any disabilities / mental health / physical health problems. It will not be able to affect the way they view for application. The way it works, is that if you are offered a conditional place, you THEN (all applicants) undergo an occupational health questionnaire. Includes all past and current health problems, with the idea not to be punitive but to make sure that they can help and support with anything needed. It's only in very extreme cases that occy health may refuse people or suggests postponing until a health condition is more improved.
Please don't worry. Please go to the GP and get the help you need. There are many, many students and doctors who have sought help for mental health problems, and it will make you a better doctor for having sought that help and looked after yourself.
Best of luck.