The bumps are very red and so is the surrounding skin, they are only.on.one arm and I.think.it could.be flee bites as I have picked up and carried an outside cat with.this arm, does anyone believe this is correct?

Kind of hard to agree with you, or make a determination that they are in fact flea bites when we can't actually see them. Cats can be infested with other bugs other then fleas.