7c is a
standard mouthpiece.
You should try a 1/ 1/2c or 3c mouthpiece.A no-name brand can be easily found on e-bay for about 20$. The tone will be better and you will be able to play longer, but mostly in lower register.
If you are Trumpet *1 then keep your 7c.
I think you're problem is the warm-up.
I had the same problem as you. My teacher told me to warm up, at first i was like Huh shut up... the next year, I had no choice but to listen to him.
So yeah, Warm up 5-10 mins before practice. First, buzz with mouthpiece(about 30secs) then, play long low notes on the trumpet. And then do scales and arpeggios, slowly going higher and higher.
And
What's the highest note you can
hit ?
And what the highest note you feel confortable playing in a song?
-Warm up
And if your chops hurt or bleed, thats good. But let them heal before playing again. The more it hurts, the more you are improving your higher register, but dont overdose
°~Gxy