Do you think I am mentally ill?

I know everything I am about to list makes no sense and is not healthy, but I honestly CANNOT help myself. I'm not being dramatic, I honestly cannot stop myself from doing these things - if I could help it, I most certainly would stop. Here are some ways my obsession about germs causes me to behave:

If I have to use the bus to get somewhere or go to the public library to use a computer, I ALWAYS wear a pair of gloves so not to touch anything directly.

I refuse to eat anything if I have to touch it with my hands. If I cannot use a fork and knife (or spoon) I will not eat. At work I don't eat anything on my break because of this, so I usually go about 8 hours after breakfast without anything to eat.

If anyone uses a pen or pencil of mine, or if I even drop it on the floor, it must immediately go in the garbage afterwards.

Washing my hands until they are rubbed raw from soap and hot water.

I open doors in public by covering my hand up with part of my shirt or use a glove.

Do you think I am mentally ill?