I would see your doctor and describe to him what is going on. Are you experiencing any other symptoms since you started on the shots? Since you already got the pap smear that's a good test to take and the fact that there's nothing abnormal about it means that you're probably OK.
A friend of mine who went on shots reported something similar and she eventually had a complication in her gall bladder and had to have it removed. It's very rare, but if you start feeling ill or start bleeding excessively then see your doctor. You indicated that it is like a period ... is there a significant amount of blood, like a period? Or is it just a little, like less than a tablespoon full?
Did your doctor give you an explanation for might be causing this? Sometimes women bleed a little during sex if their partner is large or if the sex is too rough. Hopefully some women here who have had similar experiences can give you some better insight / advice.