Choking baby

Mi
So, my son chokes. He has choked on 3 separate occasions, on VERY small, soft foods. 
First time - 2 kernels of fully cooked rice
Second time - The dissolving baby puffs that looks like Cheerios
Third time - Shredded chicken (less than the size of a pea)
This was not gagging or anything like that, it was silent and he was not getting any air... he was CHOKING. I had to yank him from his chair, swing him over my legs, and pummel his back to get the food dislodged. 
He can definitely chew and wasn't distracted. Since birth he has also kind of coughed a lot, but when I asked my ped she said babies just cough sometimes. 
I'm beginning to think the two things are related, maybe enlarged adenoids that may be preventing him from swallowing properly? Another clue that this may be a throat issue - he snores. 
This has really prevented him from moving forward with getting 3 meals a day and we really rely a lot on formula still. Now that he's almost 11 months old, I think that's not enough because he is just the WORST sleeper. Hungry constantly - and who could blame him?
I know GAGGING is a part of learning to eat, but watching your baby choke is not. I'm going to speak to my pediatrician again and ask for a referral to an ENT, but has anybody been through similar?