Once we got on the boat, the dive master explained that there was a strong current, but that we would be doing a drift dive over the wreck site. I was assigned to a group with a buddy, per normal, and was excited to start. ... The current was so strong that it kept carrying me and eventually the divers were out of sight. So, I did what I was trained to do, I surfaced and signalled for the boat. It took the boat almost 20 minutes to see me and honestly, I was scared that they never would.
Good for you. You made a decision to take care of yourself, followed your training, and safely completed the dive. I am curious - when you were on the bottom, trying to crawl back to the wreck site, were you fully negative (all the air was out of your BCD), or not? That makes a big difference. You really can't kick against a strong current. But, if you hunker down as close to the bottom as possible, and get fully negative, you can usually pull yourself along against the current. But, if you are only slightly negative, or neutral, chances are you won't be able to.
Greek:
I can tell you that being on the surface for 20 minutes waving frantically for the boat was probably the scariest 20 minutes of my life.
I can imagine. Many of us have been in that situation at one time or another, and it can be a bit unnerving for a newer diver, until you come to understand how drift dives work. You go in, you drift along, you (and your buddy) surface when you reach an agreed upon point / time / air pressure. The boat follows bubbles and picks up divers as they surface. By the way, did you have any surface signaling device - a 'safety sauage', or a whistle, or a mirror - with you? If not, you should. I don't usually go in to open ocean conditions without one, even if I can see the shore from the site. You really aren't all that visible in the water from a distance if you are floating at the surface. It may be very easy for you to see the boat, but not as easy for them to see you.
Greek:
PADI dive masters are supposed to be constantly checking out for their group, and the fact that I was left alone without the dive master surfacing to find me was extremely unprofessional and dangerous, given the conditions of that day.
Hmm. I don't necessarily agree with that. Whether it is a PADI shop, a NAUI shop, or any other, there is not necessarily an inherent responsibility to be 'constantly checking out for their group' in the water, IF their assignment is primarily to point out interesting features.
Greek:
Once back onboard, . . . when I tried to confront them, they blamed me for this.
Now, you didn't do anything wrong. But, they didn't either. (I wonder if they really 'blamed' you, or merely pointed out that it was your responsibility to stay with the group.) You are a newer diver, and this is good leanrning for you. What you experienced is not uncommon in drift diving. It was not clear from your post if whether any statement was made before splashing about the group staying together at the wreck site, and then surfacing together - I suspect there wasn't, which is also common for drift dives. For a new diver, I can imagine that it was scary to be on the surface, alone, down current from the boat, wondering if they see you, or if they are every going to pick you up. But, with experience you will become comfortable. Like several other posters, I have to wonder where you dive buddy was. If there was a failure along the way, I would assign that responsibility more to your insta-buddy than to the DM.
Greek:
In this situation, am I wrong to be upset with AquaWorld? They refuse to refund me my money and are being very difficult with me.
Yes, you are (wrong). Unless there was a specific commitment for the DM to look out for you once in the water, they really are not being unreasonable at all. In fact, offering you a free dive in the future is actually a very good gesture on their part.
They did offer me a free dive in the future, but I'm not about to put my life in their incapable hands again.
It is your choice, but I think you are missing an opportunity. When you dive, you put your life in your OWN hands (which may be 'capable' or 'incapable' according to the individual diver). Otherwise, it is simply a 'trust me' dive, and there are lots of SB threads about why those are a really bad idea. They are offering you a free dive. It is a chance to see the wreck you (apparently) missed, to smooth out the relationship with the operation, to learn some things about drift diving, and boat diving, to make certain BEFORE you jump in the water, what the procedures will be.