First, Ella, as a student in the US, you are entitled to be covered by a 504 plan. if you are not on one now, you and your parents need to get a letter from your doctor that says your diabetes needs can interfere with school (ie, time to test, etc). This documentation will need to go to either your school counselor or school psychologist. These people will write up a plan with you and mom that says things like, "needs opportunity to test, needs time to address needs as they arise, etc". This is a legal document and if teachers and staff don't follow it, they are breaking the law. 'Nuf said. (I am a school psychologist )
That said - your doctor may need to write up something to the nurse more specific. It isn't really fair to make you test in class. I realize they don't want you missing class, but you could go between to the nurses' office and it would be more sanitary. The doctor can specify that.
As far as not being able to do what you need to do, you are protected by the Individuals with Disabilities Education Act, 504, and the American's with Disabilities Act. If need be, you can go to the principal with the legal information and ask that person to help sort it out with teachers and students.
I wish I had the answer for those other kids. In many cases, the less you play into their "crap" the less they will mess with you, but it is hard, I know. I've been there. You can try educating them, but it may not be worth the hassle and your time. Ignorance isn't really curable in a lot who have no desire to learn, sadly.
The good news is you are almost out of HS.