Help On the trumpet
I'm afraid it's difficult to give you any sound advice without actually watching you play. Perhaps you need to go to a local professional trumpeter to find out what they think. You say there is vey little little top lip in your mouthpiece when you play - I have very little bottom lip in the mouthpiece when I play and it hasn't done me any harm!!
Getting rid of the vibrato is a long and slow process and requires you to do lots of long note practise.