I know I"m a dumb girl, but live on my own trying to fix the sink?

So... my sink hasn't worked for a while. When i fill up one side, it goes into the other sink, and letting i drain after washing dishes takes forever. I finally have "diagnosed" wich side is the problem. I have tried plunging my sink, for a good 1/2 hour, i've tried, mixing salt, with baking soda, and pouring it down the drain with boiling water after, i tried this twice, it worked on the one side but not the other. Then i stuck a coat hanger down the drain, it would go down on the one side but not the other, so i started jaming it in, and could get it down just a tiny bit further, stuck a wooden spoon down, and on the one side it would totoally go down , but on the other not at all... so tried jaming that down, but the wooden spoon broke and i ended up stabbing my self in the hand.... so... i've sorta kinda given up. I"m a 20 year old girl, and on ODSP so can't really afford a plumer. Maybe i'm just a typical girl who dosn't know how to fix stuff... but i don't think somone will be able to snake this thing. Help?