We've been working on it all night. We tried a snake through the drain thing. And did the vinegar/baking soda/boiling water thing. That didn't work either. We really don't wanna call the plumber and we don't want to remove pipes unless we have too. Is there any other way?
Bathroom sinks clog primarily because hair gets snagged on something in the waste line, builds up, forms a nice fibrous reinforcement for soap to stick to and then you've got a first class clog. Drano will only loosen the soap, it doesn't really get rid of the hair, so it's only a temporary solution. Plus, the hair will continue to build up with continued use. Does this sink have a pop-up lever for the stopper? Those are the first places that clog. If it's a new, or even from the last twenty years, sink, you should be able to disassemble the nut where the popup lever enters the waste pipe, pull out the lever and then to go town with your choice of tool - snake, coat hanger wire, whatever, to remove that hair. I usually disassemble the trap and clean out the whole mess, from sink to where the waste line enters to wall or floor, and then it's good for several years. Don't waste a lot of money on drano or similar products - they're only effective up to a point and they're hard on the environment.
I have that problem once in a while and it always end up that there's so much hair balls entangled inside the drain. What i did is get a longish, thin and pliable but strong wire, create a small hook at the tip and try to wrangle what is suppose to be hairs inside then lift out slowly. It always work.
We had a clog in the kitchen sink, and we had to go in the basement and snake it through the pipes down there. I dont know a lot about it even though I was the one who did it, my mom knew which one to open. So I guess go from there, your snake prob. wasnt long enough, we had to snake a LONG time. Good luck, Clogged sinks suck! Edit if you snaked it and use vinegar, Draino isnt going to work.
How far down the drain did the snake go? If the plug is between the wall (where there is a vent to the outside air) and the sink, a plunger will work. You need to plug the overflow holes with a wet washcloth, get about 3 or 4 inches of water in the bowl and PLUNGE the thing. Do it violently enough so that some water slops out. That means HARD!! If that doesn't clear it. The plug is either solid (in which case you won't hear water swishing through the pipes--you clear this with your ears as well as your arms and tools and you will need to disassemble the sink drain lines and snake it out) or it is in the wall which will require a snake--preferably from the outside down.
I would confirm that the rest of the plumbing in the house is not backing up also. The bath sinks usually get clogged up with hair but you may have to take some pipes apart to really get at the problem. The ones under the sink usually are made to do this fairly easily. You may have to rent a motorized snake from a rental center to make some headway on this. The motorized snakes really are effective and inexpensive to rent. But before renting try the removal of the p trap under the sink and snaking the drain from there.