D.M.
Hi R.,
I wouldn't worry about the clorine as much as I would the sun exposure at 7 weeks. I would make sure the pool area where you will be is completely shaded or dress your baby in a full coverage suit that privides SPF protection from the sun. I personally wouldn't use sunscreen at 7 weeks especially the normal kind that works by absorption into the skin. It might be safe to use one of the topical sunscreens (I know California Baby makes one that is a rub-on stick with zinc oxide that I use on my kids faces now) at 7 weeks but I have never researched it.
Good Luck, D.