"I'm in (a) class right now" with or without "a" is better as a general statement, to show you're busy.
"I'm in THE class right now" would be if someone had asked you if you were in a specific class right now and this was your response to them.
Adding "the" in front of common nouns is almost always only used for when all people in the conversation are aware of the exact subject, so in this situation, I don't know what class you're talking about, so "the" shouldn't be used.