2cm dilated!

My doctor checked and I am 2cm diliated at 37 weeks. I was 1cm last week. When he checked me this time is caused a bloody show ( I believe I lost my mucus plug) I had to be watched over night with mild contractions . Which eventually slowed down. I'm nervous that I'm at a risk for infection without a mucus plugšŸ˜¬ also how long after bleeding and being dilated did you ladies go into labor ? Thanks in advance.Ā