It looks like my water broke last night at 32 weeks. Does that mean that labor is imminent?

What did your doc sa. Your doc should have already outlined the treatment plan for you and you should be in the hospital until u deliver, u need to be watched closely because if u show any evidence of endometritis you will need to be delivered right away, all your questions form this point should be directed to your doc and all should be answered by your doc since your doc knows your situation.
No. When your water breaks early, before 34-35 weeks, you will be given medication to stop labor. Unless there is an infection present, in which case it is better to deliver the baby, you may be able to stay pregnant until 34-36 weeks. Labor is allowed to occur or is induced at that point.