Hi & welcome to the forums. What you are describing as a kid is a coaster brake bike, 1 speed & use the pedals to brake by pedaling backward. Fixed geared bikes work on the same principle but minus the coaster brake hub but you still use the pedals to brake by going backward or you could add hand brakes. I would not recommend a fixed gear for someone that has been off the bike for so long. Nor would I recommend a fixed gear for any triathlon unless it's all flat & you are running a really tall gear.

I would look into getting a new bike or having your existing bike fitted better. It sounds as if that bike was never a good fit for you to begin with hence your frustration. You can have the stem replaced with one that would keep you more upright but that will affect your performance unless this event is just for fun only then who cares, right? As for gears I assume your bike has stem or down-tube shifters which can be really frustrating for some people. Todays bikes are outfitted with indexed shifting on the handlebars which make shifting much easier & less confusing.

You could go the route of a new bike which I think is the best for you. Go to your LBS tell them your needs & comfort level & get properly fitted for a new bike. They might even have a used bike that they could swap out components with to fit you better. If being on drop bars is still not in your plans you could go with a flat-bar road bike. With the proper stem height & length you could be sitting in an upright position.

It sounds like your really interested in getting back in the saddle, you just need the right bike.