Possible preterm labor? 34 weeks

So I had an appointment with my midwife today and I told her about how I was having frequent Braxton Hicks and a Hines in my cervix and she checked me for dilation, turns out I was “almost 2cm dilated” and got send to the hospital for monitoring.

At the hospital contractions started and I was getting them every 3ish minutes but they weren’t painful, they were however creating a lot of pressure down below. The dr came in to check me again and I was now a little over 3cm dilated so they gave me a steroid shot for her lungs and sent me home. They told me not to return unless I have period like bleeding or contractions that I can’t talk through.

Fast forward to getting home, I was still having contractions causing pressure, every every 2 minutes but they still weren’t necessarily painful. They eventually stopped and after an hour or so I noticed pink blood mixed with mucous. It’s not enough to drip but it’s present every time I wipe. I’m also still having contractions every once in a while with pretty bad lower back pain. I’m due to go back to the hospital tomorrow for my second shot and more monitoring.

Should I expect baby to come soon? Also does it look like she dropped? First photo is last week second is tonight.