31 weeks pregnant with green discharge. NO STD

So, I’ve had this discharge for a month probably. I’m std free but, I’ve been super concerned that it is an std or something awful because of the color. There’s no smell, but I have been itching like crazy! My ob didn’t seem concerned and would not do an exam, so I went to an urgent care this morning. They did a pelvic exam/ swab. He said there was lots of green discharge around my cervix, but it didn’t look like an infection. I can literally feel when I’m discharging and it makes me feel so gross. Did anyone else have this??? I’m also 31 weeks pregnant, so could doing this exam make my go into preterm labor?