Had a shot and dioxycline will that kill tricI?

No. Doxicycline won't treat Trichomoniasis. The treatment is oral metronidazole or tinidazole. The injection you received won't treat it either.
NO. Recommended treatments include: Metronidazole 2000mg; single oral dose. Tinidazole 2000mg; single oral dose. Metronidazole 500mg; twice daily x7 days.