Using the pool outside of lessons

Hello!

I (32F) have posted a couple of times as I've started swimming lessons as a complete beginner. I have had 3 sessions so far and have just about got to a point where I can float face down in the water.

My current lessons take place at a pool that is quite far from home so I have decided to switch to a gym that is closer to home. I am considering getting a membership at the gym so that I can practice what I've learned in the lessons a couple of times a week, without the instructor.

Is this a stupid idea? Is it even allowed? I don't want to get in the way of lane swimmers and I also don't want to drown lol. I'd appreciate your advice, TIA.