Being a novice diver in cold water can be hard. But let's look at the story you told, and see if it could have been a better experience . . . You said you hooked up with a local dive club to go diving. That's a good thing to do. The more you dive, the more comfortable you'll get.
You say you "weren't buddied properly". I'm not sure what that means, but that's something which is entirely within your control. You have the ability to refuse to get in the water, if you don't have a specific buddy with whom to plan and do the dive. I've done that -- I did a dive in Indonesia with three other ladies, and at the beginning, I said, "So what are we doing for teams?" The answer was, "Oh, we're not going to buddy up, we'll just dive as a group." I refused to do it, and arranged one of the other divers to be MY buddy. Good thing, too, because within five minutes, we'd gotten separated from the others. If we hadn't already agreed to work as two separate teams, we'd have had to end the dive at that point.
One of the advantages of having a specific buddy is that you can discuss the protocols you are going to use for things like buddy separation. You guys could have reviewed the standard approach of, "search for a minute and then surface and regroup". This sounds particularly easy, if the dive you were doing was that shallow.
Of course, you couldn't know what a minute was, because your depth gauge wasn't functioning. With your number of dives, I would have aborted the dive at the point I became aware of that problem. I know you said you knew the max depth of the site, but it was the timer that got you into trouble, wasn't it?
In addition, in 2m of viz, it's very important to have two people agree that one of the major goals of the dive is to stay together. In fact, it is possible for one person to do that job, but that person doesn't have much fun on the dive. But if you have an agreement to stay together, then both of you need to maintain the situational awareness to do that, which means not getting fixated on the fish or reef or wreck so long that the buddy disappears. We dive Puget Sound in low viz all the time, and buddy separations are very rare among my friends, because we all work hard to make it so.
Then you were stressed by worrying that where you were going to ascend was unsafe. This tells me you either didn't get a very good dive site briefing before you went in, or you didn't listen to it very well, or your underwater navigation skills aren't very good. A dive site briefing should talk about the bottom contours and hazards of the site and how to avoid them; you can also use your compass to understand which direction takes you closer to the rocks and which takes you farther away. Underwater navigation is a blend of information from your instruments (depth, time, and compass direction) and information from your environment -- bottom contour, notable landmarks, current direction, surge, and so on. Navigating underwater is a skill -- it can be learned and refined, and it takes practice. But you should always have a sense of what the site looks like, where you are going, and how to get back. That's part of the dive planning.
Finally, you say something about descents and ascents being stressful. This is also a skill that can be practiced. The good news is that you ARE making an effort to dive locally, which should mean "dive more often", as diving often is the only way to get good at control in the water. Many people don't practice controlled descents -- they just let the air out of their BCs and plummet. This is a common cause of buddy separation, especially where the bottom is deeper than the range you can see. If one person has to pause for dodgy ears, you don't ever see one another again. It's a very good exercise, where possible, to practice descending to ten feet and pausing to okay and regroup, and then going down to 20 and doing it again, until you get to the bottom. (Yes, there are places where you can't do this, because you really need to get down fast to stay in reference to structure, but I don't consider those dives appropriate for someone with your amount of experience, and the problems you've described.)
So I think there are a lot of things about what made this dive unpleasant for you that you can take control of and improve. No need to give up on the sport! Just be determined to set your own dives up so they turn out fun. 90% of that will be done on shore, or on the boat, before you ever get in the water.
