It's not a question of whether you'll grow to gain the abilities of interacting with others. But whether you will enjoy it enough to make a career out of it.
Also no friends? That's a bit... Schizotypal.
Yeah that's what I was gonna say. In my experience the issue is less that you won't make it through the process, it's that you'll be miserable.
Think of it this way. You should be able to make it into med school if you're social enough to be able to keep it together for a few hours at an interview. And by keep it together I mean- just be professional and non-crazy. You don't have to be an extrovert or even particularly warm, just professional and not apparently a serial killer. If your grades and MCAT scores are good enough to land you an interview, and your interview isn't a complete car wreck, you'll get in (yes, I know there's more to getting into med school than grades, but in my experience you can be pretty good at research while being pretty socially incompetent, and you don't have to say much while you're shadowing either). So ok, you've gotten into med school, maybe even a pretty good med school since you had good grades/scores and good research experience (don't need to be a people person for any of that).
The first two years of med school go smoothly because its basically the same deal. You study hard, you work hard, you're not mr popular but whatever, you're used to it and you don't need a ton of friends. You find another quiet and studious person to work with and that'll be your med school buddy, and that's all good. Trust me when I tell you, your situation is NOT unique, i can think of at least a handful of people who fit your description and they're friends with each other. Because you've been working hard, you do well on Step 1, you start third year. So far so good.
Now we've got a problem. You know a lot, but you're not great with people. Yes, you've had some practice, but it's still not what you love to do, it's not your comfort zone. Other people are way more comfortable now than they were in the classroom, while you were way more comfortable in the classroom than you are now. You're having to talk to patients all day every day, and they're asking you awkward questions you don't know how to answer. You're put on the spot on rounds or in the OR on a daily basis. And the worst of it is- your grade depends on the subjective evaluation of people. Suddenly, people liking you or not has a bearing on how you actually do academically. More importantly, you may realize that being surrounded by people just isn't your thing. It doesn't make you happy at all.
Here's the thing. You CAN go into something like radiology or pathology, but the job markets for those are terrible at the moment and you'll still have to go through both med school and residency requiring a good amount of social interaction. Those are the only two in which you genuinely can be a loner- the rest require some amount of teamwork and such.
So rather than thinking about whether your personality will prevent you from getting into med school or whatever, I'd think about to what extent it makes you unhappy to be in those kinds of uncomfortable situations- because it'll happen
a lot.