I totally understand (and agree with) all of the posters telling you not to worry since you are only 20.
At the same time, I am concerned about the fact that your parents won’t you let you shidduch-date. At one time, the normal way to have met people may have been different, but it seems to me that nowadays, refusing to go on shidduchim amounts to relying on a miracle.
It is possible that it is different in your circles. However, even in circles in which people meet on the own, they usually also go on shidduchim when applicable and appropriate. Even in the secular world, l’havdil, there is a concept of blind dates.
My grandparents, a”h, weren’t Frum, and even they met via a blind date. While, actually, my grandmother was calling my grandfather to try to set him up with another girl, and he ended up asking her out. But she was trying to set him up on a blind date.
If you felt like this system (of meeting guys on your own) was working for you, I wouldn’t be concerned. But it sounds like you don’t think it’s working and you would want to go on shidduchim if your parents let.
Is there any way to convince them? Do you have a Rav whom you can discuss this with, and maybe have him speak to them? Maybe you can ask your parents if they can let you try it once or twice (the first time you may be nervous, so maybe it should be twice) and see how it goes.
I think someone needs to explain to your parents (politely, of course) that even though it worked for them, things are different nowadays. Just like they didn’t meet the same way that their grandparents or great-grandparents did.