What Causes Pain While Inserting Tampons?

So I really need to swim for school, (because in PE it's the swim unit, and we need to take a swim test to pass) but I'm on my period and I've never worn a tampon before. (I'm a freshman in high school)
So, I decided I might as well try now! But every time I try to put in the tampon it hurts if I put too much pressure on it. and I used a mirror, so I know I'm putting it into my vagina. I looked at multiple resources and diagrams so I'm fairly certain I know I'm doing it right.

At one point I got it mostly in, but there was still a little bit sticking out and knew it wasn't in right, because i could feel it... and it didn't feel good.

I'm starting to worry that my vagina may be swollen, because sometimes when I'm not on my period, that area itches and there's a little bit of discharge.
We have swimming tomorrow, and i thought I would be off my period before then.... I guess not. Do you have any advice for me?