If there is no odor it's more likely a bad yeast infection when you get bv there is an odor and especially after 3 weeks the doctor told me bv the worse it gets the worse it smells and it's normally a fishy smell with bv
I had the same symptoms as you and went to my appointment and they did a swab and just by looking inside because of the discharge they said a yeast infection and told me to get the monistat 3, 5, or 7 day treatment never the one day treatment and they sent the swabs in and I also had bacterial vaginosis I'd call and say you want someone else to actually check and run tests or go someplace else. If you want to go somewhere else call planned parenthood and tell them your symptoms and ask if you could be seen and explain what your "doctor" said uti are rarely ever that bad and don't cause discharge they normally caude pain with peeing and stinging and burning uti has nothing to do with the vagina that is bladder and urinary tract
did she run any other tests? That does not sound right at all. And for it to be going on for 3 weeks, something else is going on. A uti would not give you green slimy discharge for 3 weeks. I'm sorry, but you should see a different doc because this one sounds stupid. It could be bacterial vaginosis or something else but don't take my word for it. Please see someone else.