Signs of bacterial conjunctivitis are generally sticky discharge, generally matted on waking, red eyes which are commonly gritty on blinking. Management with topical antibiotics, in my opinion, are too often advised and shouldn't be available over the counter. It is a self limiting condition which tests have shown the duration to be similar if treated or not. I would just advise cleaning with sterile water regularly with the option of lubricant for alleviating the gritty discomfort.
Allergic conjunctivitis is more likely to be a watery discharge with itching as an obvious sign. Again managing and alleviation of the symptoms is the preferred option - cool compresses, removal of the allergen.
Many local PCT's have introduced local enhanced eyecare services in which registered optometrists can investigate your red eye symptoms for no personal fee. The appointment is paid for by the PCT. These services are able for GP's to refer people who have presented with ocular complaints and who need further investigation but do not need direct hospital referrals. Different PCT's have different systems but a phone call to a local optometrists will let you know if there is a scheme on your area.
It'll clear up soon either. Good luck.