Schools have nothing to do with it.
Hospitals, you actually need less of to curb your average age stat. That stat, average age, is the key to natural population growth. Also, if you purchase pop, your new pop looks a lot like your current pop.
You have 2 painful choices. Except gradual population decline about indefinitely or go for a slightly lower health index and attempt to reverse the damage done to average age.
Either way, you are going to be giving a lot of that population back to the game.