That sounds dreadful! We had a not-so-awesome experience with a dive op in Key Largo...could be the same one. On that trip (in December) what struck me is that some of the crews were fantastic and others were not great. One of the big things was the OP rushing us into the water. It was all hurry hurry hurry. Now that I have more experience, I'd be more firm about taking my time. I'm not slow to get ready, but I will not be hurried along before doing my own safety checks.
So, a few things. First, ignore the directions on the box of bonine or Dramamine. You need to take it a lot earlier - like the night before for morning dives. I am prone to seasickness. I usually use the less-drowsy Dramamine (but sometimes generic bonine). I take it every night while on a diving trip and then again in the morning because I don't want it to wear off for afternoon or night dives. Only after I started taking it at night did it help me.
Second, you are a certified diver and are responsible for your kit and entry. I would be livid if someone pushed me into the water before I was quite ready to make the jump. This happened to me in Key Largo and I was pretty damn mad about it. I don't mind someone helping a bit if it's an odd entry, but don't push me to hurry me along. I'm not slow to enter. I've done some dives where a seated entry was the best way to enter (mostly cenotes in Mexico) and then I did appreciate a little lift and push, but it was offered in advance, not thrust upon me (ha ha).
If you are every uncomfortable, scared, or just not feeling it, it is perfectly OK to call the dive. Better to be on deck and wishing you were in the water than in the water and wishing you were on the boat! I've had a couple of dives that I absolutely hated. I really dislike night diving, so I avoid it. I do love diving just before dusk, so if I'm going out on a boat and those are the 2 dives, I'm happy to sit out the second. I'm going to give it one more try in August and if I still hate it thats OK.
I don't think you're doomed as a diver. You will gain confidence as you dive more and will likely be more confident in standing up for yourself in certain situations and also knowing when to call the dive. Just keep diving and recognize that just because some DM or boat captain tries to tell you what to do, (to a certain extent) you don't have to do it. (I mean, the captain is in charge of the boat, so you need to follow boat related rules, but if you're not comfortable waiting on the bottom, then wait on the surface. Yes, this may make you more seasick.) I'll note that something similar happened with me and my husband. Another diver managed to jump in with a gear issue...something that should have been caught by the diver before entry, but again, we were being rushed. So the DM told us to wait on the bottom. We waited for at least 10 minutes which really shortened the overall dive. It was super disorganized. The DM should have ensured the diver got back to the boat and then come down. That diver could have gone with the next group (he wasn't with a buddy). Next time I'd refuse and wait on the surface so as not to use up a bunch of gas before even starting the dive.
I'm really sorry you had such a bad experience. We were in Key Largo in December and the vis was really good, despite the weather not being great. (It was mostly cold and rainy.) Since we were there, several people have recommended different dive ops. I'd like to go back and dive with one of those ops instead, especially now that I do have more experience and more confidence. I really want to dive the Speigel Grove again with a smaller group.