Fellow teen here (diagnosed age 17)! I am extremely open about my diabetes, have no problems doing diabetes stuff in public and enjoy educating others about type 1. However, I have definitely had some awkward moments in public because of diabetes. I have sat on the floor in the middle of a shopping centre to check my blood sugar (got some odd looks from a lady walking by), and stood outside an opposite-gender public toilet for 20min because my blood sugar was low and that was the best place I could find to have a hypo (this was in a crowded convention centre). They weren't so embarrassing though, because the only people surprised were total strangers.
The worst moments are ones involving people you know. I wear a CGM, which can be quite noisy with constant alarms, so in public I usually turn down the volume or mute it. Recently I was in a lecture at uni, and my CGM vibrated on the table. The lecturer heard, thought it was my phone and asked the class whether I should get a penalty for my phone going off (he has a mobile phone policy that he explained at the start of session). I had to explain that it was a medical device and not a phone. He knows I'm a type 1, and after class he came up to me and apologised, but at the time it was super embarrassing because I was having a bad blood sugar day and I hated explaining it in front of everyone. I get good grades and always participate in class, so I don't know why he decided to pick on me that lecture, maybe he was just having a bad day or something. It doesn't feel embarrassing anymore, just a funny thing that happened to me, but at the time my blood sugar was a bit high and I was mortified that my blood sugars had interrupted class.
Another one was at the local chess club - I've played there for years and know the other players pretty well, and we're a very casual club in that phones are allowed to be turned on (usually in chess electronics are banned due to cheating). I have my CGM on my phone and was looking at it during a game, which I eventually won. My opponent complained about my phone use afterwards (saying that I could have been looking at a chess engine) and I was almost penalised with a loss, even though I offered to let them look at my phone and check that I wasn't cheating. I was pretty offended that they thought I would cheat, firstly because I've known them for years and thought they would know my character better, and secondly because I was the strongest player at the club and so winning the game was not unexpected. I'm over it now though - still good friends with the guy who accused me of cheating (if anything I probably played worse than usual that game because I was a little high). Funnily enough, I was recently playing a game with the guy who runs all the tournaments here, who is a huge stickler for rules. I tried to explain about my pump and CGM before the game, expecting him to be suspicious during the game if I didn't show him the devices, but he said not to worry about it and that he trusted me. So everything went better than expected!
So don't worry about taking care of diabetes in public - good people will be sympathetic and even try to help you out, and if people think worse of you for being a type 1 then they're not worth knowing anyway. Usually, other people won't even notice you checking your blood sugar or taking a shot because they're only thinking about whatever they're doing. And if you do get into trouble like with your teacher, most people will be understanding if you explain the situation.