Is there any other way of a getting trichomoniasis other than sex; example weak immune system from sinus infections, staph infections?

See answer: Trichomoniasis, a parasite, is almost always passed on sexually. Trichomoniasis can also survive on infected objects like sheets, towels, underwear, and sex toys and can be transmitted by sharing them, though this mode of transmission is quite unusual. A weakened immune system may increase your susceptibility to this or any other STD. Although symptoms vary, most men and women are asymptomatic.

Trichomoniasis: Regardless if a person has a weakened immune system, they would still need to come in contact with the trichomoniasis parasite to become infected. The normal routes of transmission for Trichomoniasis are penis to vagina, vagina to penis or vagina to vagina. It would be very uncommon to get it through a non-sexual route (like an unclean sex toy)