You need to remember and keep in mind that the air BCD expands as you ascend. The closer to the surface you get, the faster the ascent. That’s why you were unable to stop when you involuntarily started rising on you second dive. At shallow depths, this usually isn’t a problem, but could become a major one and cause you harm if it happens at depth during a lengthy dive. You actually need to bleed off air as you ascend to maintain the same level of buoyant air in you BC. The less air you have in your BCD at depth, the better off you’ll be. You may find you can reduce the amount of weight you carry, also. When I first started, I was carrying about 18 lbs in fresh water, but was having to fill my BC with a lot of air. I had good bouyancy, but I was susceptible to sudden rises like you are talking about. I was also using a lot of air due to the drag I was creating in the water. I started reducing the amount of weight I carried and am now down to 10 lbs with my configuration. My SAC rate has gone down dramatically and I can move about in the water column as I want without fear of rocketing to the surface.
I’m also rather perplexed at your saying it would have required a lot of unnecessary work to stop your ascent. How so? I don’t see how pressing the purge button on the inflator would be unnecessary work. And simpler still, most modern BCD inflator hoses have a cable attached to the shoulder dump inside the hose so that all you have to do is pull on the hose to release air.
Anyway, as Eric said, welcome to the wonderful world of diving. You’ll get past this (or should, anyway) and you’ll be the better diver for it. At least you recognize a problem and are willing to work on it.