I started taking Monistat yesterday and then got prescribed antibiotics. Can I take both?

Yes. Yes, they are for different things and the Monistat may help prevent candida overgrowth while on the antibiotic.
Antibiotics/yeast. You can take both. A probiotic such as acidophilus tablets twice daily is always good to take when on antibiotics. They contain the healthy bacteria that populate the vagina so help prevent yeast infections.
Yes. Most oral antibiotics will have no effect on topical Monistat, the exception being oral antifungals like Diflucan (fluconazole). Since both drugs treat the same condition, duplicate therapy would likely not be necessary.