Should I be trying to get my 10 month old to a ENT he has had multiple ear infections and constant green stuffy runny nose all of his little life?

Probably. After mutliple ear infections in infants is a good indicator for continuing ear problems, so i would talk with your pediatrician first, i'm sure he has concerns as well. If he has concerns I am sure he will recommend an ent.
Likely. My mantra is "five in a year or 1 that won't clear" ( in 90 days) would get an ENT referral and expect tubes.At some point the gunk in the middle ear gets so thick it won't clear & removal during the tube procedure is the only way to clear them.