From personal experience loss of mucus plug was the onset of labor. I would rather be safe than sorry, since you're 35 weeks and not days - it's not so early in your pregnancy that you just could not begin labor. I wouldn't rush to the hospital but I'd still be cautious.
Why would you go to the hospital cause you lost your mucus plug? Lol. Woman can lose and regenerate their plug multiple times. I would phone your OB maybe and see if they want you in for another check up. Or if you start to get pain, diarrhea, vomiting, or obviously consistent contractions. Then you should head in to L&D.
You should go to the hospital , it sounds like you lost your mucus plug !! Better safe than sorry