3 month old puppy still has green snot?

I got a 3 month old black lab mix puppy from the humane society 3 weeks ago and since then hes had green snot coming out of his nose. Hes been to the vet 4 times since ive gotten him and they have said hes had 2 URI's and now has bronchitis. The vet has given him 2 rounds of clavamox (14 days worth) for his URI and also hydrocodone for his bronchitis. I'm not sure what to do anymore this is getting to be extremely expensive for me, and he has another vet appointment in 2 days. He's out of clavamox now but still has hydrocodone, should i get him more antibiotics when we go back to the vet in 2 days or should we try to let it go away on its own?