How to take a gap year in high school? ?

There’s no such thing as a “gap year” in high school.  I suggest you and your parents talk with your doctor(s) and school district to find out what your options are.  I’m sure you are not the only student in the district with this type of situation, and they should be able to help you figure out what to do. (504 plan, homebound/virtual learning, etc.)

There is no way they can legally make you come to school with the circumstances you are describing. 

If you are in HS and are going to be staying home, get an online HS program. A 504 plan may help with that.

But you can not take a gap year.  You can do an online program at home, you can drop out of your meet your state’s requirements, but you can not just sit at home for a year 

As a parent I would be talking to my child’s doctor too. 

maybe your doctor can write you a note

ask your doctor to write a note about it

If you do not already have a 504 plan, get one. Then make sure one of the accommodations involves not coming to school when you or your doctor fee it would put you at risk.

They can't make you physically go to school if it would risk your health. If they try to push back, contact a local TV station and tell them your story. I find it scary that there are clueless schools out there. 

There are plenty of people in a normal school year that can't be physically in school for whatever reason (i.e. really sick, injury, etc) and the 504 covers that.