My son had his adenoids and tonsils out in June and he snored quite a bit until the swelling went down, about 3 days post-surgery.
You might try propping him up on pillows when he sleeps and see if that will help him in the mean time. Definitely check with the doc though.
Best of Luck and I hope your little guy feels better soon. Mine recovered quicker from his surgery than the illnesses that led up to it! Hope you situation goes that well!