If you can find a Pet-Insurance in the US that is worthwhile, please let us know, because I know that myself and many others on this forum have looked into all of the major ones available throughout the years (Nationwide is really the only major one still in existence), and none of them have even been close to worth the cost of the premium, at least not for birds or reptiles.
The first step is always verifying that your CAV/Avian Specialist accepts the insurance you're looking into, and if they don't, then ask them if they accept ANY pet insurance, and if so, which ones. And then research each individual insurance plan.
Unfortunately, in the United States, when it comes to pet insurance, what you're going to find is that it's never worth the premium at all, especially when the pet you have is not a dog or a cat. There used to be a lot of different pet insurance companies out there (up until the last few years when they all went out of business), and what I always found with all of them was that they had plans that covered the most common, routine procedures and treatments that would only apply to dogs and cats, such as vaccinations, neuters and spays, etc. When it came to the emergent, expensive things, like surgery, x-rays, blood-work and other lab testing, etc., none of them covered anything, or they wouldn't cover anything until you personally paid-in a certain amount of the bill, which was at least $1-2K, and then at that point they would pick up the rest of the bill...
Now, the only major pet insurance company in the US is the Nationwide one that you're talking about, and again, for birds, reptiles, rodents, primates, marsupials, etc., everyone that I've known that has looked into it has decided that it wasn't worth it at all, as once again, it doesn't cover anything at all that pertains to birds or other "exotic" pets, and the only time that it would become worth the price of the premium is if something very serious were to happen to your bird, and it only kicks-in after you personally pay out of pocket a very large amount...So as a result, I don't know of a single person who has looked into it for their birds or reptiles that has opted to get it. Not one.
Usually what most people do is either use their Vet's in-house payment plans (if they offer them), or their in-house insurance (if they offer it), or they simply take out a credit card that is only for pet health/medical emergencies...You're much, much, much better off taking out a regular old credit card for this, even if it's at 21% or higher, than using Care-Credit, as Care-Credit is actually considered an "unsecured personal loan", which means that there is no cap on the APR, and I think that the typical CareCredit rate, regardless of your credit score, is around 28%! Now CareCredit is great if your credit is bad and you can't get approved for a regular credit card, because they are much more lenient about approving people with bad credit than the credit card companies are. So CareCredit definitely has it's place. But if you have even mediocre to bad credit, you can usually still get approved for a $1,000 credit card at a lower rate than CareCredit is...So that's typically the way to go if you have no cash flow...
Or, the better option, as already mentioned, is to start right now saving up a fund that is not to be touched except for your pet's medical needs. Just throw in either a set amount each paycheck, or even just throwing in whatever you can throw in whenever you can, it really does add-up. Hell, I have a huge change jar thing that I decided last year to take to the bank and put through the change-couting machine, it was the place that I tossed all of my change when I walked in the house (I have it right by the inside of the door), and it had over $500 in it! So there ya go, that paid for all 4 of my guy's wellness exams that year!