Nanelline: it is often tricky in some areas still to access or find emergency contraception in some areas, and unfortunately, yours is certainly one of the tricky ones.
Here is what the Princeton EC site (which has a wonderful tool on that page for finding what EC options are available in every country) lists as available to you in Panama:
Oral Contraceptives used for EC / Progestin-Estrogen Combined
Note: in 28-day packs, only the first 21 pills can be used
Take 2 pills within 120 hours after unprotected sex and take 2 more pills 12 hours later:
Nordiol
Ovral
Take 4 pills within 120 hours after unprotected sex and take 4 more pills 12 hours later:
Microgynon
Nordette
In other words, those are the combination birth control pills available there which can also be used as emergency contraception. Your doctor CAN give you a prescription for these pills. But if you cannot get into the doc's office fast enough, you can also try to track down any friends who use those birth control pills, and would be willing to help you out. Those would be the ideal pills for you to use right now, and the most likely to be effective as EC.
My contraceptive bible that I rely on for issues like this does not list Provera anywhere in the reference per EC. Provera is generally used for women to promote uterine bleeding. But it is a progestin, and I'd concur with the doctor and the nurse that this does present a possible option for you. Yes, one thing, in lower doses, Provera can do is to prepare the uterine lining for pregnancy, your body already does that now, anyway, but at higher doses, it will prevent ovulation, which is the mechanism of it which could help you now. Looking at the information on it, I see no greater risks of long-term problems or side effects with it than with Plan B or other emergency contraceptives, or with regular birth control pills for daily use. Certainly, as usual, pregnancy presents greater health risks to women than any of these medications, especially used in such a limited way, do.
I do see you as having a substantial risk here, because you're at the end of your cycle, and sperm can live in the vagina for several days: if you ovulate earlier in your cycle (which you can only know if you chart your cycles), then this timing presents a substantial risk.
If you cannot find anyone with the birth control pills which can be used for EC in your area that I listed for you, then I would suggest that you call into the doctor or nurse your boyfriend spoke to and ask them about this yourself. If either or both of them advises it, I would suggest you use this, since it sounds very clearly like a pregnancy would be a very real problem for you. From what I can gather, the largest risk taking this would present for you is simply that it won't work, you know?
That all said, I'm also really concerned that this happened at all. IF risking pregnancy is absolutely something you cannot do, then using withdrawal as a birth control method is beyond ill-advised. Withdrawal is NOT a reliable method of birth control, and you've unfortunately discovered. If you and your partner cannot even obtain and use condoms, then I'd advise you to simply abstain from intercourse at this point. And if your parents discovering you are having any kind of sex would be an end-of-the-world scenario for you, than I'd advise you abstain from all sex, period, until you're out on your own and the potential consequences are just not that disastrous.
P.S. Just so you know, having intercourse doesn't alter your menstrual cycle or period, unless you become pregnant. Only becoming pregnant has that power. Sometimes, some women will see some flow changes from intercourse during menstruation, but that's only because of uterine contractions, and jiggling everything around in there. But it doesn't even cause a period to stop: that's a very involved chemical process in your body which is not controlled by your genitals or what someone else does with them, unless that results in a pregnancy (and even when it does, that'll happen only after a period is through and simply cause you to skip periods thereafter).