That advice is solid, but I'll add: healing your followers does speed it up, but if you want it actually fast without mods, use the Restoration exploit. Cast a healing spell on yourself, then use a damage spell (or just let enemies hit you), then heal again. Yeah, it's still kind of tedious, but it's way faster than waiting for Lydia to take damage in combat, and you can do it literally anywhere - doesn't matter if you're in a dungeon or standing in Whiterun.
The perk they mentioned that lets you cast while moving is called something like "Regeneration" or "Continuous Casting" - honestly not sure of the exact name, but it's early in the tree and definitely worth grabbing. More importantly though, grab the one that boosts your healing spell magnitude first. On higher difficulties, a weak heal spell is basically useless, so getting that damage reduction early makes the playstyle actually viable instead of just you standing there watching your health bar.
One thing I'd push back on though: don't sleep on the Undead-specific healing spells if you're fighting Draugr or vampires a lot. They're technically Restoration spells, so they level the skill, but they're way more fun to use in combat than just spamming Healing Hands on yourself. Makes it feel less like you're grinding and more like you're actually playing a healer build.