Not a doctor, but based on my child's countless colds which landed him overnight in the hospital once and on oral and inhaled steroids twice (all before he turned 18 months old), I would definitely go see a doctor if you are concerned. (Turns out our son has cold-induced asthma aggravated by mold we found in our home.)
The congestion itself is uncomfortable, but kids will naturally breathe through their mouths if their nose is stuffed up. I highly recommend using saline drops (make at home or purchase) and using the Nose Frida -- a Swedish snot sucking product (http://www.nosefrida.com/). It sounds gross but it works better than the suction bulbs which can be too strong. For extreme cases, your doctor or the pediatric ward of the hospital has mechanical suction tubes which easily clear our noses for kids who can't blow their noses yet.
The wheezing is more worrisome. It means he has fluids in his lungs and may have trouble breathing. When our son was wheezing, he was still happy and chipper and we didn't really worry. Shortly after that thought, our doctor suggested we get to the hospital asap. So we learned the hard way that children having trouble breathing and aren't getting enough oxygen in their bloodstream work harder to breathe and lose a lot of energy and liquid by breathing hard through their mouths. Some bad signs to look for:
- Breathing faster than normal constantly (depends on child, but getting over 35-40 bpm was worrisome to our doctor; my son is at about 28-30 when healthy)
- No urine / few wet diapers over a day (getting dehydrated == very bad)
- Retraction at the base of the neck below esophagus or below ribcage: if it looks indented as your child breathes, this means they are working really hard to breath. When healthy, there shouldn't be any hard sucking in that causes the retraction. (Check your own body out to see.)
Again, when in doubt, go to the doctor.