Sink drains really slow. Pipe is pitched upward?

Okay so this has been an issue since I moved in but the slow drain has gotten worse the past few months. At first it would pool a bit but generally drain within 10 minutes. Now, an entirely filled sink takes over a day to drain completely, which is gross.

I've avoided using that sink as much as I can but I really would like to have a kitchen sink again. I noticed when I first realized there was a problem that the pipe leading out of the u-bend is pitched slightly upward and figure that has to be a contributing factor

Here is the pipes under the sink. Another angle

Is this something I can fix myself? If I need a plumber, is it going to cost me a lot?