None of these is really how I would use those prepositions. Others might think they're fine. Here are what I think are more natural versions:
It's now two hours past my appointment time that I've been waiting.
I had to wait for two hours for my appointment, from 2 until 4 pm.
It's been two hours since my appointment time, and I've been waiting all that time.
It's now two hours after my appointment time, and I've been waiting.
They all mean more or less the same thing, but the usage is different because they imply different relationships with the appointment time. Here's a different set of examples:
It is past sundown.
It is after sundown.
It's been a while since the sun went down.
It's now three hours from the time the sun went down.
I guess the short answer is that you should not think of these as interchangeable but instead learn the patterns where each applies.