Right medical receptionist here( well trained, currently working at a homeless hostel), we are not little Hitler's we simply have rules to go by doctors available, slots available etc. You can ask for an emergency appointment the same day and insist on sitting there until you are seen.
Alternatley as above mentioned see a nurse, or insist on speaking to one, they can usually be found, i have had to do this myself from time to time with residents and i ahve demanded to speak to a nurse. It can be done, hang on in there you need to see someone, a continual bleed for this amount of time is more than a little worrying.