I agree with what others have written, the key is going to be the level of your playing when you apply to the program, whether you have a BM degree or not won’t matter, lot of musical kids go to universities, study privately, get a degree in something, then apply for an MM and so forth.
Like @momofadult, what I am concerned about is your playing level now, for a very good reason. Getting into a top BM program on violin is extremely difficult, and by the time you are applying for MM or DMA programs, you will be competing against kids who probably were doing intensive work before college on violin, then spent 4 years focusing on it in conservatory or a college music program, and be competing against kids from all over the world. I think the biggest thing you can do may be to get a skills assessment from someone who knows what the levels are (perhaps your current teacher knows, but to be honest, a lot of teachers think they know what the level is, but don’t). If you school has a music performance program, or a teacher who is well known, you may want to try and get an assessment from them, or if not, try another school in your country known for high level music, even if you have to travel.
Especially since you have been studying medicine, which I assume takes a lot of time, you will probably not have been practicing the way the kids who are studying music do in college, which means you will have an added handicap there. It is why the assessment is important, it at least tells you if you have a realistic chance of getting into a competitive program for a masters and/or DMA. The key thing there is competitive, there are a ton of music schools out there now that offer MM’s and DMA’s, and many of them will actively recruit students, sell them on the idea the program is a ‘top program’, and the reality is, to be bluntly honest, is that the kids getting into the program are going to have an even more tough time making it coming out there, if your desire is a career as a musician. They have programs and especially if kids are paying for it, will recruit almost anyone (note, I am not talking about the school that encouraged you to audition, since I have know way of knowing which school it is, or how good it is).
It doesn’t mean if music is your dream not to try, but as momofadult said, go into it with open eyes and know as much as you can as possible. If your skills assessment shows that you are near the caliber to get into a top MM program, for example, and if the school you are talking about has a decent teacher, and is also going to be affordable, then you may be able to go there, then build your skills enough to get into a great DMA program…but if your skills are only ‘good’, it may be a very tough sled, to impossible, to get into that top program doing an MM anywhere…
Things have changed a lot in music over the last 30 years, 30 years ago what you want to do would probably be a lot easier than today, and violin is especially bad because there are just so many wanting to play it (primarily because it is a solo instrument, it is like Piano and Cello and Flute that way).Back then someone could be an okay player in high school, get into a pretty high level program, then get into a decent career, that isn’t true any more, the number of jobs have dried up that used to be there, and it takes a lot of perseverance and networking and hard work to put it all together into a career, it was hard back then, it is difficult today, that is the reality. as @momofadult pointed out, getting into that top level MM program or DMA program these days guarantees little, other than you probably are pretty accomplished, the real hard work is what happens after. It isn’t like kids getting DMA’s from programs like Juilliard et al go to a placement office and there are a ton of offers for jobs, it doesn’t work like that, the difference from coming out of those programs is likely the talent and skills are refined to a very high level, so when competing for jobs, they will even be considered. Some make their own careers, and there someone less accomplished may be able to create something new, form their own ensembles, but when going after standard jobs, auditioning for ensembles, orchestras, etc, gig work, it often comes down to the best player.
If your dream is there, pursue it, there is nothing wrong with pursuing something you know is difficult, it is one of the horrible things about these times, that people are afraid of trying and not making it, if you pursue it and it doesn’t work, other doors open up:). Go into it knowing that, going into it knowing where you stand compared to others is knowledge, and knowledge truly is power, it lets you make plans, navigate, otherwise you would be finding your way blindly.
I wish you luck!