my gym's pool

Yesterday I tried to go swimming at my gym for the first time. Its summer here in Buenos Aires which means that its about 90 degrees and humid every day. What that really means is that its WAY too hot for my Upstate-NY ass to go running. I decided that the pool would be a much more comfortable work-out option. Little did I know how much would be involved...
As everything here seems to be unnecessarily complicated I had the sneaking suspicion that there might be some hoops to jump through here as well. Two days ago I asked the girls at the front desk if I had to do anything special to use the pool. "No just go in", they replied.
So yesterday I got into my bikini and headed over. I went upstairs to the womens locker-room and looked (unsuccessfully) for the pool entrance. I asked the attendant there.

A: Do you have a card?
Me: What card?
A: Your pool card. You have to go back downstairs to reception and get a card and then get checked by the doctor.

So, I went back downstairs, got a card, and then went back upstairs to the attendant. "Ok, I'll bring you to the doctor now", she said. This is where things got really strange. He checked if my feet and hands were webbed. (Is it good or bad that I don't have webbed feet? Wouldn't I swim better if I did?) Then he checked my armpits. I still have no idea what that was for. I guess I passed because he signed my card and sent me back to the attendant who finally showed me the way to the pool.
I got down to the pool and handed my card to the lifeguard.

L: And where's your swim cap?
Me: What? I don't have one.
L: No swimming allowed without a cap.
Me: You've got to be kidding me.
L: Go back to the locker-room and see if the attendant has one she can lend you.

So, back up to the locker-room I went. When I got there the attendant said, "Oh you don't have one? I figured you did." I wanted to shout at her "Lady, I'm standing here in a freakin bikini at the gym's pool. I don't even have a real swimsuit and you assume I've got a swim cap?!?!?!?"
Anyways, she handed me a swim cap and some goggles and I went back down to the pool. I handed my pool card to the lifeguard for a second time.

L: And you can swim?
Me: Yes.
L: Ok, hop on in. If you share a lane stay to your side.

What????? After all that you don't want to see if I can actually swim??? How much sense does that make??