Once I hit the level cap, will I be unable to level up my Health, Magicka or Stamina?

That is correct. Once you can't level any more, the only way to increase health/magicka/stamina is from gear or spell/potion effects.

As of Patch 1.9 of Skyrim, a level 100 skill can be made legendary, resetting the skill to 15 and refunding perks spent in the skill. A legendary skill can be leveled again, which will result in more perk points. This can be done for each skill as many times as you want with as many skills as you want. It is theoretically possible to get all the perks in the game and have a huge pool of Magicka, Stamina, and Health.

More details can be found here:

https://elderscrolls.fandom.com/wiki/Skills_(Skyrim)#Legendary_Skills

Here:

https://en.uesp.net/wiki/Skyrim:Skills#Legendary_Skills

And here:

https://gaming.stackexchange.com/a/176751/174247