Is there a highest amount that you can level health to?

900 base HP assuming you hit the level cap which is 81. You can enchant armor for roughly another 70 HP total. And then there's alchemy pots.

I'm pretty sure you can go far above just an additional 70 HP through armor enchantment.

You get +72 HP on the chest piece (the only piece of gear that can be enchanted for HP) with +31% or+32% enchanting bonus potions, which are only obtainable
through a full gear set of +28% alchemy bonuses (4 x 28%). This is with 100 enchanting/100 alchemy and all the relevant perks.