Yes, you do have time to go see the doctor and to have a blood test. A blood test takes 5 minutes. Loss of weight and loss of appetite are very serious symptoms and should be thoroughly checked out by a doctor immediately.

It is never healthy to skip meals. And, it's not healthy to have a job that keeps you so busy that you don't have time to take proper care of yourself. It sounds like you are overworked or are not up to the rigors of your career. Have you considered changing jobs?