For the sake of discussion, let's not rule out fleas. Just because you haven't seen them doesn't mean they aren't there. You simply go buy some Advantage and put it on your cat and the fleas should be dead in 24 hours. If the red bumps start going away it was fleas.
It might be skin lice. cats catch it allot my neighbor rescues cats for a living and she gets them all the time. they wont do anything to you just bath your cat in pet friendly lice remover and use lice soap on you. then apply some rash cream on the bumps and it should go away! these are not contagious so it is safe to go to work or to the grocery store.
Sorry to disagree with you but, if he lived outside, I would be very surprised if he doesn't have fleas. Trust me on this, you don't always see the fleas but they can affect the cats behaviour, so a quick trip to the vet or at least a phone call, would sort this out for you!
It suggests an allergy. But since you have a new cat, it is useful to always have a new cat checked by a vet for a health assessment. That way you will know no fleas, no worms, and no ear mites.
That way, those are ruled out for certain.
Cats secrete a protein in their saliva, and that protein is a potent allergen. And not all cats secrete the same amount. So a shelter cat could have minimal amounts, or more. Cannot be predicted.