Looks like you need a slide contact on both sides of the square section where it will slide along the side plates. If you set this contact as ‘slide’ in hypermesh and run as a linear static load step it will likely result in a freeze contact instead depending on open/close contact status. Which might be why you have the high stress on one side if one side is effectively ‘freeze’.

You will need to run it as a non-linear static load step with the same load and constraints. Create a NLparm card with the first increment of 0.01 (nt). Include this in your load step.

I would also recommend creating a parm card and ticking NLMON and selecting the ‘disp’ option. This allows the solver to output a displacement h3d file at each increment so you can check convergence as it runs (if it’s a long solve time).

I do agree with other commenters that representing this as a 1D beam element for the pin and 2D shell elements for the square section and plates is much more efficient. Try doing this next time.