Exemptia for ankylosing spondylitis result in dry scaly skin and rashes. Does it indicate psoriasis?

Hello doctor,

I am a 41-year-old male, an old case of ankylosing spondylitis and was on Methotrexate for 10 years, then switched over to injection Exemptia and after six month of injections, I started developing skin rashes and dryness and lost hairs on my both the legs only on the outer side. I have dryness and itching on my hips both the sides, on neck underneath jaw on both the sides. One rheumatologist suspected psoriasis, while dermatologists said dry skin. Injection Exemptia was stopped immediately after I develop nose infection which some ENT people diagnosed as vestibulitis while other said anterior atrophic rhitnitis. I was switched back to Methotrexate and gradually I had to stop that due to chronic nose problems. I am on long term nasal antibiotic ointments. Once I stop it nose problem immediately worsens. Joint pain is still there but mild. I have stopped Exemptia for more than a year and Methotrexate for more than six months. Still my nose issue is persisting. I started developing tiny pustules around my nose and face, chin, neck, and on thighs as well. I am attaching all the images. Please let me know if it is psoriasis or pustular form of psoriasis or chronic furunculosis or some other condition. Which investigations are required? Do I need antibiotics or immunosuppression?