I see you looked it up already but yes most universities pools will be olympic since they don' have 6 year olds needing to go 25m in competition
I'd work on your kick but it should not be a focus, you need your legs to bike and run not your arms so you really want to concentrate on keeping your kick to a minimum, just enough to keep you afloat and going straight. Just like the stroke should be long and deliberate so should your kick, don't kick from the knees only. IF you want to use a kick board get some fins to use, not only will you skoot across the water super fast which is fun but they sort of force you to have good form, if you try to kick from the knees with fins in on they don't do much, use your whole legs and you'll really feel the difference with the fins as to what is right and wrong.
Really longterm you should look into using a pull buoy so you can focus on your stroke and being efficient without kicking at all, right now though its honestly probably dangerous and would not suggest it.
For now just slowly get laps in, getting the distance covered while not sucking up all your energy should be your goal, you will get efficient automatically for that to work.