My 2 yr old is on polymyxin b sulfate and trimethoprim antibiotics eye drop if we don't finish it will it cause a super infection later?

I do not think soBUT: Please ask your pediatrician if you don want to continue the treatment. I do not have the knowledge of the reason why this antibiotic is prescribed. But completing the course of treatment is desired to clear the infection without recurrence and relapse. Super infection is usually not a problem,if you mean bacterial resistance, that is always a possibility

Should use till: it is gone unless directed otherwise by your doctor. If you stop early the infection may not be eradicated and will flair up off the antibiotic.