I didn't really know where else to put this, but my 12 year old son really likes to play PM and he's really good at it. He says he wants to play the game competitively, but I'm not sure if I should let him. He's really good at the game and all, but I feel like when he goes to tournaments, He'll be overwhelmed by everything there. He's a really shy guy, and I'm not sure if I should let him. What are your thoughts on this?
Yes he should go! He'll get to meet people when he plays, and depending on his skill level (be it quite good as you say, or on the lower end if that's the case), he'll get plenty of complements or tips to improve.
You should tell him to be receptive to criticism/advice from players better than him (there almost certainly will be if he has not been able to play with others) and not to try to claim to be the best or anything like that - people who do so come off as obnoxious and don't endear themselves to others (obviously). That said, shy people rarely do these things so I'm sure this isn't a problem.
There may be some rude people, but that is not the vast majority of smashers (and he's playing PM, which insulates him from criticism from his game choice to a very high degree), and I know when I was new, everyone was nothing but helpful and willing to play me a lot (even though I was much worse than almost everyone there).
For what it's worth, I know a 14-year old in MN (where I'm from) who is considered the 5th-best player in our area (on a rankings chart), and people always welcome new smashers, skilled or unskilled, to expand the scene and (if they are really good) help increase the overall level of the community. And the largest Brawl tournament of 2014 (Apex) was won by a 17-year old. So age should be a non-issue here.
I also do not think you need to hang around - you can if he asks you to, but most of his time will be spent meeting people and playing Smash, so he'll probably quickly start feeling right at home.