I swam a few hours ago, I love it. My grandma taught me during summers with her in the Catskills. I have to wear goggles, I cannot open my eyes at all under water. If you are going to shower afterwards you might want to bring flip flops you can wear in the shower, especially if it is an indoor pool. Is it indoor or outdoor? Towel for sure. I get paranoid about the tremendous amount of chlorine in indoor pools, so I always bring along clothes that I am not too worried about if they fade, and I rinse my suit and role it in my towel to go home. But I think maybe I am the only person in the world that worries about such things. LOL.
Some tips: keep your fingers together and hands slightly cupped, think of it like having boat oars in the water, if it had slats instead of being solid you would not move as quickly through the water. You have to breath out to be able to breath in, which means while your head is under the water you are blowing out, learning how to breath is liberating, it is just as important as your stroke. I am against the idea of a nose clip, just me. There is no way to get water up your nose if you are breathing out when you are under the water.
Don’t be nervous, many many adults learn late in life to swim. I think it is fantastic that you are taking lessons. It takes some practice, give it time.