2003 Chevy 1500 5.3

Okay, i have a 2003 Chevrolet Silverado 5.3 v8. Its got high
mileage, but recently, i had issues that i thought was my
transmission, but had two mechanics tell me its not the
transmission. Upon taking off, it doesnt want to shift out of
first, i have to get the rpms up to around 2500, and let off
the gas and itll shift as it idles down. The motor runs great
and really strong. And no other issues with shifting once i
get going, no slips or anything. Sometimes taking off, it
does sound like its struggling for air or something!  One of
the two mechanics told me it was throwing out breathing
codes. I replaced the mass air flow sensor, and air filter, i
just dont know what else to check or try. But i also dont
want to spend a bunch of money trying to figure it out, lol!
Anybody else have these issues or worked on something
with these issues?