the doctor says my cholesterol is too high

[Plug Drugs]

you have to pretty much abstain from all carbs to enter ketosis

That's where you're wrong, your body can be in ketosis and ingest carbs simultaneously, as long as that level of carbs isn't large enough to cause the body to begin storing fat rather than burning it.
It's like when you eat a lot of carbs, your body tells itself "wow, we've got all this energy to spend, and then some, well we better store some of it for later"
and that's when your body stops ketosis.
Just don't bomb your system with carbs.

if you do go into ketosis you have to have fats in order to survive, not the long-chain fats in your reserves (though they still get burned) but medium-chain fatty acids like omega-3, or short-chain acids produced from metabolizing fiber

your body is built to go long periods without eating anything; we were hunters/gatherers about 20,000-30,000 years longer than we were consumers.