I've never really felt shame for playing a character. I think it's a running joke in NJ that Marth is the worst character in the game, and I used to main Marth, but I just shrugged that kind of thing off. I also feel like most of the time people are joking when they make those types of comments, and if they aren't, then they're kind of as$holes and idk why you are around people like that.
It's one thing if people are mocking your Falco, it's another thing if you're just not good at playing. Ever heard of trash talk? If you ever go to a tourney, you better expect it if you plan on getting a good placing. Even if you have a good Falco, people will sh*t talk you to try and get in your head/throw you off your game. Based on what you've just said, it sounds like trash talk would be very effective against you. Know that trash talking is another type of tactic employed in any competitive environment and know that getting mad/frustrated is only playing into the opponent's hand. For me, I don't like to do what people want to manipulate me to do, so it's much easier for me to deflect those sorts of remarks. Granted, I haven't actually experienced trash talk at a very high level either.
Now, if you're actually playing poorly, then that's a different matter. It means you aren't good enough, and you need to get better. And if people are making fun of you for it, it's kind of a **** move, but it has some truth. Instead of getting hung over those types of comments, however, you should use that as motivation to improve yourself. I mean this is kind of where the cheesy life advice comes in, but use their antagonism as your motivation.
Now confidence boosters, I can't give you any, because I don't know you personally, so I don't know any of your other redeeming qualities. All I know is how you play brawl from the videos you've posted. If you're looking for me to give shallow compliments, I won't, because I think you played poorly in the videos you posted recently. HOWEVER, I think the standard to which I am judging you on is much more extreme, and if you are just looking to get better than the people around you/your friends, then I think you can do that as long as you polish up on your mechanics. Falco is the type of character where you can be good by just being able to perform all his little techniques and tricks. Keep that in mind, and I hope you are more successful in the future.