Firstly, 'Apply Scale' to each of your objects - this is important for any simulation.
Secondly, in your particular case you don't need to enable self-collision since the cloth isn't looking to be at risk of hitting itself. The self-collision will slow down the simulation and can cause its own problems if its parameters aren't appropriate.
Thirdly, 'Apply Scale' on your 'frame' objects and check the direct of the normals - you need to ensure they're pointing 'out' of the faces, not 'in' (otherwise the collision will be in the wrong direction). In your case the bars of the frame are quite thin - reduce the 'Inner' setting in the Soft Body And Cloth collision settings - you currently have it set to 0.200 and this is quite large for a "thin" structure such as this as it can result in the 'back face' affecting cloth at the opposite side of the bar.
Fourthly, ensure there are no overlapping meshes at the start of the simulation as this can cause significant problems as the simulation attempts to eject the vertices out of the collision mesh.
Don't forget to clear any baked simulation and re-run it to see if this helps. If this helps you can then start tweaking the simulation by re-enabling self collision (if needed) and potentially increase the 'Inner' and/or simulation quality. If this doesn't fix the problem, please post a video of the new behaviour.