If it's a 2007 182 then it is fuel injected. I've known of other new Cessnas having (intermittent) starting problems related to fuel supply issues.
Two points:
1. Your aircraft is still within warranty if a 2007 model so to mess about with it will more than likely cause warranty issues.
2. If you intend putting your and other's little pink bodies in the aircraft for the purpose of flight and you don't know whether your aircraft is carburated or injected then may I respectfully suggest that you aren't the person to try and fix it. Best to leave it to a qualified engineer and if you aren't happy with the service you are receiving, best get in contact with another engineer.