What does a spotty red rash on my arm mean? The rash has small red spots and is bumpy.

Many things. A common condition is keratosis pilaris (kp). Small reddish bumps appear on the back of the arms and sometimes the front of the thighs. It is very common and not dangerous. If you are unsure, please see a dermatologist.
RASH. While a picture is worth a 1000 words, a rash needs to be seen. Words spoken or written will not do.