Welcome to the forum. Yes, it is normal in a new gunite pool for the ph to rise. Using acid to lower it is exactly right. As far as a time range on receiving your test kit, unfortunately, it sometimes takes awhile to get it. Ben has had a multitude of problems this summer and is doing his best to get kits out all the while working and trying to keep the forum up and running. The latter has been a real pain for him recently as he has had numerous hackers causing him problems. The kit is worth the wait, however.

Enjoy your pool and that new baby girl and congrats!