Erik had his removed at 4, Anders at 2 1/2. Erik was like that--when he got sick his tonsils closed off his throat and I worried about him breathing. He was never given steriods, though. Both of them had tonsils that were completely touching even when they were healthy. Both had them removed for sleep apnea.
Anyway, yes, it could be allergies. And if he's always had a strong gag reflex (Erik did, too), it could be that his tonsils are always large, and then get too large when he's fighting an infection.
I would want to know if it were an infection that could be treated, or a virus. It's critical that your child be able to breathe

so I would want to know what to do to insure that. (will antibiotics be helpful instead of steriods?) Does he have sleep apnea issues? I would want him healthy and then I would monitor that.
Anders' breathing was always strident, he was a HUGE mouth breather and you could hear him from the next room. I'm sure it has to do with allergies, too, in his case, as he has them, but the sleep apnea was pretty significant.
I hope your pediatrician is helpful and responsive!