Yes, it is possible that you can get re infected with Trichomoniasis if your partner has not finished his course of antibiotic treatment
Trichomoniasis is a vaginal infection caused due to a protozoan trichomoniasis vaginalis and the treatment involves the treatment of both the partners. The protozoan commonly exists in the seminal fluid of the male partner although it does not cause any clinical symptoms in the male partner. Hence, it is imperative that your partner completes the course of antibiotics.
I also suggest you do the following things.
1) Vaginal douche with warm water with a few drops of vinegar is recommended to reduce the inflammation and the discharge. It also helps to irritation in the vagina.
2) Complete the course of antibiotics before any sexual activity.
It's also recommended that you get a vaginal smear to make sure that you are clear of the infection.
3) Maintain safe and healthy sexual behavior to reduce the chances of sexually transmitted disease.
4 ) Use condom regularly both as a contraceptive as well as barrier for infection.