What you say is true, beta blockers can exacerbate or even cause psoriasis.
Alas, almost every drug has rare side effects...but the side effect isn't rare if you are the one who gets it.
It is possible that you had the defective immune system and the beta blocker merely pushed you over the edge, instead of the next irritant to come along but you;ll never know for sure.
I hope it gets better for you, psoriasis can be a nightmare to live with.