I'm glad you are going to the doctor's to get checked out. You could have a gastrointestinal bug causing the initial nausea, vomiting and loose stools. Incontinence can happen during pregnany due to the rapid changing abdominal space and pressure on your bladder. The stomach and back pain can have multiple causes, but still need to be checked out. If you have leaked amniotic fluid, it can reseal itself, but that's not a guarantee. If you are in pre-mature labor, they will try to do as much as they to prevent delivery. If you are in labor and they can stop it, you will probably be on bedrest and medication preventing contractions for the remainder of your pregnancy. This does not mean you are for sure in labor, but I do want you to be aware that in the event that you are, what to expect next.
A baby at 20 weeks is too small to survive, so they will do everything possible to prevent delivery. Babies have a chance of survival starting at about 24 weeks.
My prayers are with you that you just have a bad stomach bug and after some fluids and rest, you'll be feeling much better.
I have no experience with this as i am a ftm but just wanted to say i hope all is okay with you and baby and good luck.