Would this help Busters allergies?

Ok, so my 8yo started licking/knibbling/scratching resulting in hair loss around ears, belly hind legs, neck and he seems to lick his paws more than normal too. This all started in November. I let it slide for a couple weeks to see if it would go away, it didn't. Took him to the vet and they gave him a allergy shot and said that it's seasonal, food or behavioral. The shot did seem to work for a couple weeks but the licking/scratching ect came back. Ok, so I then switched foods using Natural Balance Duck+Pea, no change going on 2 weeks.

My question- It seems very possible that when the furnace started getting used was when this all began.  We also had a little flood in the downstairs over the summer so there may be a little bit of remnent mold spores hanging out down there (Where he spends 75% of his time). Would buying a hepa air purifier and putting it in his room help? I am also considering changing the furnace filter to one that helps with allergens as the one in there appears to be a basic do nothing filter.

It may help, certainly couldn't hurt.  Figuring out allergies can be difficult.  Since medication did help I think you are certainly dealing with an allergy rather than a behavioral issue.  Have you tried a different litter as well?

If it was a sudden onset, look at what changed around the time of the onset of symptoms.  My first question was going to be about litter.  Did you change his litter?

Tell me about it, it's a costly adventure.

Litter and food had remained the same. The only thing I could think of was the furnace kicking on blowing all the vents out. Since the shot did help I almost have to think whatever it is, is airborne.

But at the same time, he isn't sneezing or wheezing, just the licking/scratching/hair loss..

Have you changed his food recently?  Did you change the litter?  These types of symptoms are usually related to food and/or litter.