How can posterior scleritis and sinusitis cause proptosis and how to manage in that case?

Very rare: In 45 years of practice, I have never seen chronic sinusitis produce scleritis. I am presuming this is a disease of the eye. It is certainly true that acute ethmoid sinusitis in children can produce life threatening infection of the orbit, so called peri-orbital or orbital cellulitis. Let us know what you mean more specifically by "scleritis."