Miraak’s cult is still there

This sounds very much like a bug. The Black Book in question is merely one of many, and all but one of them grant three choices, of which you pick one. Also, your main level should never, ever go up except via leveling skills, so if your skills weren't increased at the same time, it's 100% a bug. And unless you're made a skill Legendary (see below), 81 is the normal cap, so your skills would need to be basically all 100. Even if they've increased, though, it's basically guaranteed to be a bug.

As to your side note, yes, there is a way to get more perk points. Skyrim patch 1.9 added the ability to make a skill that has reached 100 Legendary. This resets the skill to its base level of 15, while also giving back the perk points that skill had (since many of those perks are ones you're no longer qualified for). Because the skill was reset, you can level it up to 100 again, gaining character levels as you go.

Additionally, if you're not willing to give up your skill levels for more perks, you can simply complete the main Dragonborn questline. The rewards at the end include an ability to reset the perks on a tree at a cost of one Dragon Soul. Your level in that skill remains as it was, but all the perks are refunded. It's not quite the same as gaining new perks, but it can be very useful for things like fixing mistakes, and also refunding perk points on crafting skills. You might not want to reset your Enchanting, in case you need it again, but you can reassign the perk points for a while. If you need your Enchanting perks again, a quick trip to Solstheim and a couple dragon souls is all it takes.

Try using resurrect 1 on her in the console, followed by disable, enable if that doesn't work. Also try sending her off and waiting 30+ days before returning to her.