Can i get examined by a gynecologist while on my period?

Of course: As a general rule, there is no time of day, time of month, nor time of year when a doctor cannot examine a patient. Depending on what the patient's symptoms are, what her underlying medical issues are, and what the doctor is trying to assess, there will be optimal times and less desirable times to examine a person. Note that a gynecologist can examine any and all parts of the body. Details matter.