Constant congestion is a pretty good sign there is something allergy related going on.
When Bear was about 6 months I knew he had allergies. The stand in pediatrician (ours was on maternity leave) said no, babies that age can't have allergies. So I gave him allergy medication in the correct dose for his size and voila! no more symptoms. Our Pediatrician came back and agreed with me...
Also people can grow into and out of allergies, so periodic testing if there is concern isn't a bad idea.
About the school part, I've learned a hard lesson about letting it go. Wolf used to love worksheets, would do them for hours. Now that they are a part of "school" he complains that he has too many. Basically what I have done is stop giving him any work I'm pretty sure he knows (not perfectly, just pretty sure) except every once in a while for review. I also let him know that it is review to make sure his brain remembers.
If he knew the math in the car, why do it again to make sure? He's already shown understanding. If he likes doing it in his head, why make it more concrete than that? Most of our multiplication work is all mental. Wolf is just not into touchy-feely math. If your guy gets upset when he doesn't get it immediately, say "fine can you think of another way to figure it out?" It stops being about not knowing and becomes about problem solving. Example: 17-9=what Ok, well what+9=17 gives you the same answer right? You know how to do it that way.
Also I know a lot of people are mentioning time and I don't know if you have mentioned how long you "do" school in a day. Wolf is in 1st in Independent Study and I specifically asked how many hours a day should we be aiming for. She said 4 and that even not doing any "real" schoolwork (sitting down with worksheets, etc...) we would probably surpass that with no issues at all each and every day. Reading books, talking about animals or the weather, running around on the playground, going with mom to vote, etc... All of that counts, so your stealth teaching idea should work great! So much time in a conventional school is taken up with organization and waiting. It's really mind boggling to realize how much.
