Cervical check, mucus plug?! Thoughts?

So, 39 weeks, 5 days today (Monday 5/24). Went into the doc office to have a cervical check as I’m set to be induced Wednesday and she wanted to see if I dilated at all so she could figure out what steps she wanted to take for my induction.

She checked and said I was only 1/2cm dilated and only like 40% effaced. This check was more uncomfortable than before as it felt like she was swirling her fingers up on me. After she was done she asked me to come in tomorrow to get a balloon inserted but also asked if I wanted a pad as I may spot. I passed because every other time I never spotted. Well I got home, went to the bathroom and I had stretchy pink tinged mucus on the toilet paper with 2 little blood clot specs.

Is that part of my mucus plug? Did her check knock some loose? Is that a good sign that maybe things will pick up on their own?!

First time mom here!