Don't add anything to the water. I doubt the pH will continue to rise. Heck, it could be a false reading if there is any stray electricity in the water.
Do you have a pH test kit? Can you test a sample of the water in a separate cup/container with the probe?
If you aren't dosing anything to the system, there is no reason the pH would continue to rise forever. The numbers are not in any danger zone currently. Actually, I don't even believe them, unless this room is wide open to constant fresh air around the clock.