drop off = fall asleep

I must have dropped off means "I must have fallen asleep.". As kriorbi says, the statement implies that it was unintentional by use of the beginning phrase "I must have". We would say the same thing using the phrase "I must have dozed off." . In the United States, "dozed off" would be more typically used, but "fallen off" is also used.

The phrase you're trying to identify, "I must have dropped off", is actually written "I must have nodded off". And your first answer is correct - "I must have fallen asleep".

The first one means you went to sleep, and the way that it is written implies that they went to sleep unintentionally. The second means that that you fell down, though I don't know why it is written as 'I must have'. Most people know when they fall down so it doesn't make much sense.