Epipens are
explicitly allowed. You might want to mention it to a TSO before sending the bag through the x-ray.
If the Benadryl is 3.4 fl oz or less it can go through like any other liquid that's 3.4oz or less. If it's over 3.4oz, you'll need to tell a TSO about it and you might want to bring a doctor's note saying that it's
medically necessary.
TSA won't care how many carryons you have. That's purely an airline question. I think most airlines treat a diaper bag the same as any other bag of a similar size.