They would test the fluid--it has a different pH than urine and looks different than vaginal secretions under a microscope.
There are a couple of rationales given for wanting moms to head to the hospital as soon as their water breaks. The first is the risk of cord prolapse--the umbilical cord gets "flushed" through the cervix with the gush of fluid and can then be compressed. That isn't a risk for you at this point since you are trickling not gushing. The second rationale is that once your water breaks you are at risk of bacteria making their way up into the uterus and causing infection. The risk increases with time. But ironically, if you go to the hospital, you will almost certainly have vaginal exams which have been proven to increase the risk of infection AND you're more likely to pick up infections in hospitals than at home. All that by way of saying that even if it is your water trickling, there's probably no good reason to rush into the hospital at this point.
Of course, you should talk to your caregiver though.
Best wishes!
Liz.