No, but birth control pills can affect Alprazolam...
"Oral Contraceptives—Coadministration of oral contraceptives increased the maximum plasma concentration of alprazolam by 18%, decreased clearance by 22%, and increased half-life by 29%."
What this means is that the Alprazolam stays in your system longer and in a higher concentration than normal. Since this medication can, in itself, have side effects, these side effects may be increased with this higher concentrations in your system.
Keep in mind that while you are on the Alprazolam it is HIGHLY recommended that you not become pregnant (thus birth control pills are a good idea if sexually active) and that you not breast feed if you have an infant.
Yes. It is unlikely you are having a menstrual period but rather abnormal vaginal bleeding due to some other medical issue that may have nothing to do with menstruation. It would be a good idea to get this looked into medically.