Do you count contractions....

So this morning (I'm 38+4) I noticed brownish discharge that from others pictures and its consistency I'm assuming its part of my mucus plug. At the very least the thinning of my plug. I go to Dr for my weekly check up later today about 4 1/2 hours from now, so yes I'll run all this past her. Last week I was 1cm and soft ready to go by her words. Anyways backt to my question. I have had strong contractions at a rate of MAYBE 3-4 a day over last week. However after this morning I keep getting these little ones that are yes painful but not quite the take your breath away kind. So do I count those on a contraction counter? Trying to make sure for later I have a good count to give her and/or know if they are just my body's way if starting labor. Any input ladies?