The cause of your tooth infection must first be understood. Is it due to deep tooth decay?
Probiotics will not be able to help where decay has become so deep that it has infected the pulp or nerve in the center of the tooth. In such a situation, root canal treatment would be the appropriate treatment.
I have found a particular kind of probiotic designed specifically for dental use helpful in the management of periodontal infections (gum disease). This probiotic is a chewable lozenge used twice a day for 3 months.
It changes the bacterial population in your mouth so that "good" or benign bacteria overwhelms disease-causing bacteria.
Please note that these probiotic lozenges need to be used together with procedures like scaling and root planing that physically remove the calculus and plaque which is the cause of gum infections and periodontal disease. Severe gum infections may also require antibiotics and anti-septic mouthwashes.
There is no report I know that states that dietary probiotics like yoghurt, kefir or kombucha will prevent tooth decay or periodontal disease.
As both tooth decay and gum disease is caused by bacterial plaque, prevention is done by daily oral hygiene i.e. careful brushing and flossing. A healthy, balanced diet, low in sugars is also helpful.
In any case, if you have a tooth infection, don't delay in getting it treated.