Can you go to the doctors for a checkup if you're sick?

The major exception that would cause you to be prevented from coming into the office, would be if you viral symptoms and had recently returned from West Africa. You might be asked to stay in your car until staff can evaluate you and you might instead be referred to your closest hospital after the eval, or you might be referred immediately. Different practices/clinics will have different policies regarding potential Ebola infections.

I'm not sure how you know you have a highly contagious illness without having first been diagnosed by your doctor. And you would have to gone inside to get diagnosed. Some practices/clinics have "well" waiting area and a "sick" waiting area, and some will take obviously sick patients into an exam room when they arrive. You would have to schedule an appointment and while doing this, you should mention that you're sick so staff will be expecting you.

If you have an active infection, you can't have a checkup. You may be treated for the illness, if this is appropriate, but a checkup has to wait.

Yes, but you need to make the receptionist aware of your illness immediately so they can make the proper precautions. In reality, if you think you have a highly contagious illness like the measles, you need to contact your doctor over the phone and ask for their instruction. You also have to consider other people, you don't want to risk infecting someone else. My suggestion is that if you think you are infected with a contagious illness, that you contact your local hospital ER, and ask them what you need to do. An illness like the measles is VERY easily passed from one person to another, and special precautions need to be taken to be sure that not only you are safe, but everyone else. It all takes the infection of one unsuspecting person and the next thing you know you have a full outbreak on your hands. It may sound like a nightmare scenario, but the Ebola outbreak in Africa started with a single person, and ended up sweeping across central Africa.

YOu need to call first so you do not infect the staff and other patients. FYI, measles is a virus and there is no treatment.

No you should not go for a check up. Your vital signs and other indicators could be off. You could also expose other patients to the disease.