Has he tried blowing his nose? I say that in all seriousness. Unless the doctor said NOT to, I would have him try it.
My son, around that same age, ended up with (just don't know HOW it got there, lol) a little clear button thing up his nose. It was a plastic clip off the blinds cord. :( Go figure how he got one off the cord and up his nose, right?
So anyway, I really didn't think he had anything in his nose, because when I tried to look, the thing was clear plastic. It just looked a little shiny way up in there. LOL
I had him use one finger to hold the other nostril closed and asked him to blow hard out his nose. It flew right out! (good thing I stepped back before he blew). Now, this little button thing was smaller than what you sound like you are describing, so if your doctor said don't blow, then obviously don't. Also, when my son blew, I could still see a tiny bit of the object...so it wasn't completely inside his sinus....it was still lodged in the nostril, just waaaaayyy up there.
It may not work, obviously. But if it does for you like it did for us, it'll save you another doctor visit and possibly surgery. :/