My daughter had the same problem, but my doctor was pretty sure that it was from allergies and not because of adnoids. We just hung in there until she was 4 (that's the age we were told that the allergist would see her) and found out that she did have an allergy to a mold in the ground, but that she also had such a deep infection that she was put on the 20 day cycle of amoxi(unsure of spelling), instead of the 10 day cycle. She will be 7 here in a few weeks and we haven't had a problem since. She was 6mths when she went on prescription decongestant by the way.
We found out from the allergist that we could have brought her in as early as 1; however, they tend not to recommend it as allergies can change.
Also, just a side note, your child doesn't really have a "sinus infection" as they don't develop sinuses until they are 2. We were told this by 6 different doctors - 2 were allergy specialist.
We are going through this again with our son who just turned 3 and we are getting him into the allergist this month (we are not waiting until he is 4). However, our son's situation is a bit different as our family doctor moved away when he was 18mths and we are working on a 3rd family doctor (one we really, really, really like). Anyways, in our son's case, he was being treated for the wrong things which made the situation worse. We ended up taking him off all meds and with in a week he was breathing better than he has in the past year. He may have a day or 2 here and there of congestion, but nothing serious and we don't give him meds for it.
You might want to seek a 2nd opinion and see what you can find out 1st so that you can go in armed.
Hope this helps!