Hello. This is Dr. Love. The system says that you have requested a new expert.
Yes, the HPV vaccine is safe. But any vaccine can have adverse effects. For any vaccine, administration is considered appropriate when the benefits outweigh the risks. The most common adverse reactions are minor, such as injection site reactions, but the most serious potential adverse reaction is a severe allergic reaction. However, there is no evidence of benefit above age 26, which is why it is not advised to be administered after age 26.
As for birth control, fertility of women in their 50s is actually quite low, even when still having periods. Your fertility is even lower once you have gone 4 months without a period. There have been rare cases of spontaneous pregnancy in women that have not yet gone 12 months, but it is very rare. Since it is so rare, many doctors are hesitant to use a contraceptive method that has potential side effects, but it would be fine to use condoms until you have gone 12 months without a period.
If I can provide any additional information, please let me know. The system also says that you have requested a phone call. If you still desire a phone call, please let me know.