It's really important to phone the hospital and they will definitely want you to come in.
It sounds like it's amniotic fluid and it doesn't always gush!
At 35 +2 days yes your baby is a lttle early but not so early that it will cause problems. She will very likely breathe on her own and she will stay in SCU for a night or so until they are happy she is doing all the right things. Some babies born around this time will be a bit jaundiced and need some phototherapy.
Unless there is aother reason - just being born at 35 weeks will not necessarily nean you will require intervention.

Pop those clothes in the machine and then the dryer and you will be on your way to the hospy in an hour! Pack your bag and enjoy this great adventure into motherhood!