Help needed..

Morning guys.. i m not sure if this is the place to post this.. but feel free to moved to a more correct place if it's not..

Okie, here's the thing.. Yesterday night, my female hamster, Cheese was found with blood on her underside and eyes.. there was another hamster in the cage as well.. a male, Bacon. Bacon is alright with no outside wound or anything and it normal but fearing the worse i decide to put them apart..

At 1st i tot Bacon bully Cheese. End up a while later i saw Cheese sitting down with eyes open, not moving.. even though i coax her to move she also dun wanna move... after while when she left the spot.. i saw some bloody stuff on the floor. I presume she pass motion on the floor just now.. But the thing is.. as far as i saw, her droppings are those black and tiny dropping since the 1st day i got them. This is the 1st time i saw her "passing" such stuff. Can i noe what's wrong with her? I m v worried and stay up to 5am to tend to her needs. she seems rather active just that she pass these bloody motions.. due to the blood i gave her a little wash to keep her clean last night. Over all i noticed 2 or 3 time she pass these stuff till 5am from 9pm.Tis moring i went to check up on her. She looks okie and there r no more bloody stuff anymore. If i have to bring her to a vet, can i noe which vet would u guys recommand? I stay in Hougang and hope to go somewhere near so she can get treatment asap.