Please Help my Problem!!!!

i'm 17 years old and about 10 years ago i discovered that i had perfect pitch. My 1st instrument is piano so naturally my perfect picth was in concert C.

i then began learning the saxophone about 4 years ago as a second instrument and started learning on a Bb tenor. Anyone who has perfect pitch will now completely understand the problem i have. when i read music for the saxophone i am hearing a different note in my head than what i am supposed to be playing. if you asked me to play a piece of music in concert on the saxophone i could do it straight away as an A on the saxophone is a G to me. This is fine if i'm playing solo, but when i come to play in ensembles at college and i am given a part in Bb it means that i have to constantly transpose everything i am playing down a tone. it means that i am concentrating so hard on the notes i am playing which means that my rhythm, articulation and all other parts of playing falls apart.

Is there anyone who has managed to overcome this problem or knows a way of overcoming it or can give me any advice at all?