So I went to the doctor Monday of this week and found out I was 2.5 dilated. It is
Thursday. I was 35 weeks Monday and I turn 36 weeks Friday. I am just wondering since I am already dilated and my mucous plug came out if I could be going into labor soon. I do not feel like the baby has dropped yet. So how many weeks could this take. Or days? I don't want him coming until at least 37 weeks or more.

You are entering that anytime stage. You could very well continue on for several weeks still. Many women will walk around already slightly dilated in the last weeks of pregnancy, while others will be checked, find their cervix is firm and closed then they go into labor four days later.

Try to relax and enjoy the last several weeks of your pregnancy. Pamper yourself, finish last minute things you want to take care of, put your feet up now and then and get your rest now while you can!