You're not supposed to rinse with warm water, or maybe it was no rinsing at all on the first day. The warm water can loosen the clots that have formed. Also, no drinking from a straw, as it creates a vacuum, which can also loosen the clots (feel free to make comedic vacuum-related comment here).
I recently had my 2 upper wisdom teeth removed. I was also very uneasy going in as I had never had any teeth pulled either. Mine went about as good as it can possibly go though I think. Both my wisdom teeth were fully erupted (not under the gum, completely out and in place like a normal tooth), so getting to them was easy. Once they had me all nummed up, and started putting the tools in my mouth (uck, more jokes on the way), both teeth were out in less than a minute I'd say. Felt like he was poking this thing really hard into my tooth, then it was out and I was shocked at how relatively quick & painless it was.
I drove myself home, and it took a little while to get the bleeding to stop, and it was a PITA to re-apply gauze as I couldn't shape the stuff right as it felt like I was almost choking on the gauze. But the bleeding stopped for the most part after a couple hours post-removal. And I never once took any pain killers, no aspirin even, I just didn't have any pain really. The only thing that was sorta sore, was if I tried to open my mouth wide, as the spots were swollen a bit, and that caused some discomfort. 3 Days after the removal and I was eating pretty much anything/everything I had before. I put this off for quite a while, and now that it's over, it wasn't even remotely as bad as I was envisioning it might be.