I'd be surprised if it was the horn. I had a Graftonite mouthpiece for my TJ alto and it was like blowing through a straw. Once I'd changed to a Meyer there was no problem. Get yourself down to a decent music shop and try out a few different mouthpieces before you change the instrument.
I think you should get ya sax checked over and if that's ok check your mp and reed combo.I find them free blowing sax's.

