Obviously, extreme caution should be used if anyone's considering ordering medication online, because unlike most kinds of goods, it's not possible to know whether it's what it should be when it arrives. There are too many scammy or unreliable people doing this kind of "service".
I've left a note for my colleagues so that someone with more US-specific knowledge (I'm Europe-based) can say anything further you might need to know about that aspect.
That sounds like a rubbish situation for healthcare access! Overall, it's much better to get medication from an in-person provider than ordering it, so I'm going to suggest a few trouble-shooting options - apologies if you've tried these already! Often, doctors don't want their patients to go without medication just because they can't get another prescription in time, because they know that's not in the best interests of their patients. Are you still able to access the provider who prescribed the pill for you previously? They might be willing to write you another prescription to keep you going for a couple of months until you can get an appointment. Also, some doctors' offices can arrange telephone consultations with a doctor (especially one you've seen before), which might be enough to get you another prescription. Have you explained to the doctor's office that you need a refill on a prescription that's about to run out and you won't have your medication any more, and that's why you need an appointment and another prescription quickly?
When switching from one pill brand to another, the people who are best placed to advise you on what brand might be best for you are healthcare providers: really, it's best to get a healthcare provider's recommendation that's personal to you and your own healthcare information.
Some general information on switching pills: there's no difference in effectiveness between one brand of combined pill and another. There are slight differences between the formulations and amounts of hormone, which make a difference to the kinds of side effects that some people experience (but not others), and some people's bodies and/or other health needs get along better with one kind of formulation than others - it's an individual body thing! Different formulations are equally effective at preventing pregnancy. Sometimes, some people experience some temporary side effects when switching pill brand while their body adjusts to the change, similarly to how some people can have side effects when starting or stopping the pill. When switching from one combined pill to another, changing brand in itself won't impact your contraceptive coverage: you'd just want to make sure that you don't have any extra placebo days between them than you normally have. So yes, starting a different brand of pill on the day you would have started the old one is the right way to do it
Of course, if you want the extra peace of mind of feeling super-sure, you can always back up for a while with a second method like condoms.
