Does getting a rash from amoxicillin necessarily suggest mono?

It's a decent bet... Amoxicillin is notorious for causing rashes in patients with mono--it typically looks like a dense, deep red, symmetric rash esp on the chest, back, and abdomen, but elsewhere also. It is different than hives, which are scattered, irregular raised "welts" that itch badly. You're perfectly correct that the rash merely suggests mono, but doesn't prove it. You'll want to confirm it with lab tests.