The usual way women guess that they might have BV is a bad odor, especially right after their period. I'm not sure I've ever heard anyone say they had white discharge associated with BV. So, in answer to your question of whether white discharge could be a side effect of BV, my guess would be no. But the part of what you are saying that puzzles me is why did you think Rephresh Gel would do anything at all to cure BV? BV is a bacterial infection, and is not solved by gels that are basically designed to make the vagina smell fragrant. A clumpy white discharge could be a yeast infection. Have you tried a yeast-infection product from the pharmacist? If you have and you still have a problem, you might check in with your ob/gyn and get swabbed.
The discharge of BV is often whitish, grey and watery. That you used rephresh was not a good idea. Washing out the vagina can actually make matters worse because it washes out the good flora we need for balance. White discharge is okay unless it smells bad or you are itching. You can always have the discharge swabbed to find out exactly what it is which might not be a good idea in this case. Let us know how it goes.