Doxycycline and Topical Clobetasol Propionate for guttate psoriasis flare-up, back and shoulders have stubborn & unresponsive "folliculitis" now?

I'm sorry. but this is the type of specific problem about which helpful advice can only be given if a specialist in psoriasis has the opportunity to examine you and your skin and review comprehensively what treatment has been given and it's effectiveness. Only then can further suggestions for treatment be given. Please continue working with your Dermatologist or get a 2nd opinion. Good wishes:)
Guttate? Probably just psoriasis, not guttate. Different approach. Sometimes there is poor response to usual therapy for any psoriasis. There are a variety of modern treatments available for you and your dermatologist. Try some SUN.