Periods and school swimming

I only got my period at the start of this year and have had 5 already. They come every 20-22 days. Where I live, we’re going into winter. My school pool (which is outdoors) was getting fixed during summer so we couldn’t do swimming then. This term (which will be pretty cold) we are forced to do swimming lessons at school 3-4 times a week! I’m actually traumatised from last year swimming when it was freezing. So now I have to deal with freezing my ass off and having a period while swimming. Now there is one big problem. I can’t use tampons. Yes, I have tried MANY times but I just can’t fit one up there. And personally, I don’t really feel ready to start using tampons yet anyway. I could go buy some really small tampons and try again (I was trying using regular sized ones) but I have no idea what to do if they don’t work. My PE teacher is male so it’s not like I can tell him the truth. Also since I got my period really late compared to all the other girls in my class (I’m 15), they all can use tampons I’m pretty sure. I could fake an injury but my school is likely to ask for a medical certificate. Please help me out!

EDIT: we also have to sit in front of the teacher in our bathers while we do the role and get instructions for up to ten minutes.