I didn't have a waterpik when I first came out of hospital, I too had sponges (mine were pink) which helped and I did a lot of rinsing my mouth with warm water. I also used a lot of tissues to spit into..

The waterpik is a great investment as it keeps your mouth clean and can get the saliva that hides around your mouth. If you get the opportunity to buy a waterpik (amazon is a great place to shop) then get one that has a tongue scraper as you'll be able to pull the thick stuff that is sitting at the back and then rinse it with warm water from the pik.