The giddings and webster medium shank stainless steel mouthpiece (In which i paid 160 for) with a custom engraving, doesnt fit into my trombone, my trombone is a conn 50h, is there anything i can do?

I'm just now seeing this, so you may have already solved your problem. If your G & W mouthpiece is truly a medium shank, then it was designed for a European-style euphonium. Standard for most trombones today are small shank and large shank mouthpieces. The Conn 50H has a .522 bore slide. Many instruments with that bore size have a small-shank receiver and the limited research I've just done hasn't pointed out whether they had small-shank (like small-bore horns) or large-shank receivers (like large-bore tenors or bass trombones).

You might be able to find out for sure by doing a thorough search on The Trombone Forum. (I just reviewed the first couple of pages of search results.)