For the past 10 days my son is sneezing coughing and had a temperature 37.4?

Possible allergies: With no fever and persistent symptoms of congestion, it may be a case of allergies. If your son is old enough, you might try a 2 week course of an antihistamine like loratadine. Consult your doctor if symptoms don't respond to this, or if fever or difficulty breathing occurs

Sneezing and cough: Temperature of 37.4 is normal, so no fever. You can help him by keeping his nose clear. Using saline nasal spray to keep the mucus thin and clear it with a nasal bulb suction. The cough can be stemming from any post-nasal drip. This could be a cold, it could also just be a reaction to irritants (smoke, dust, dander etc). When in doubt get him check out by his pediatrician.

Temp ok: Poor guy! I don't know your son's exact age, but It looks like he's less than a year? I see he doesn't have a fever so that is good. Having a cough and cold for ten days is still within the realm of having a viral infection. He should start turning the corner and improving over the next several days. If's he's not improving by day 14 or if he develops a fever, then he needs to be seen.