The pressure is OK as is the capacity of the tank but what is needed is more flow ie. CFM. Mark Polk has a good discussion if you do a Google search for it.
The first question is why do you want to go from 90 to 120 psi?
There are $500 compressors that will do what you want to do but do you want to spend that kind of money to save time?
I run my TV tires at 65 psi when not towing and bump it up to 80 when towing. It takes about 5 minutes per tire to do that. I have the same compressor as you purchased and carry it in the back of our Suburban when camping.