Cervical checks do carry risks (look them up) so the spotting can happen. If it continues you should go back to your doctor and let them know.
I'm in this exact situation. I had a cervical check on Monday and had been spotting since, with some mucus and clotting. I called the nurse line yesterday, because I was concerned and she told me that it's normal, but to keep an eye on it. If I start bleeding heavier, I should go in. She also told me to call back on Saturday if I'm still spotting, just to check in, but that she's not too concerned about it. I also noticed that today, things are looking like they're clearing up. So I just think it takes some time.
Cervix checks can lead some to losing their mucus plugs, which it won't necessarily be clotty but more slimy... Generally if small amounts of pink/red it is okay but if ever concerned esp about the amount of spotting/consistency call your OB.