The FAR's say this on fitness for flight:

Sec. 61.53 - Prohibition on operations during medical deficiency.
(a) Operations that require a medical certificate. Except as provided for in paragraph (b) of this section, a person who holds a current medical certificate issued under part 67 of this chapter shall not act as pilot in command, or in any other capacity as a required pilot flight crewmember, while that person:
(1) Knows or has reason to know of any medical condition that would make the person unable to meet the requirements for the medical certificate necessary for the pilot operation, etc.

No where does it say you have to have a doctor certify that you don't feel fit for flight. It could be a bad headache, an upset stomach, or some other short-term illness that does not require a visit to a doctor unless it persisted for some time.
The company requiring you to go get a doctor's note, when you would not normally go to the doctor, is pure harassment. You alone have the ultimate responsibility for deciding if you are fit for duty, period. Call the union!

P.S. Questions about FAR's? Look it up at: http://www.risingup.com/fars/