usually the contents of your stomach can be broken up with that because its just half digested food and stomach acid.
so boil up a kettle full of water and then pour it slowly down the sink if you havent tried that already. also, watch out for the smell, because it aint good.
also, bathroom sink makes it alot harder than kitchen sink because you cant get at the underside. or can you? check your sink, is there a way round the back to reach the bend in the pipe? usually you can use a wrench or whatever to open it up and remove blockages, unless its built into the wall.
:edit: empty the sink of all fluids before you pour in the boiling water. also pour it directly down the hole straight from the kettle.