If you have kids at home and are worried about strep throat, check out the over-the-counter rapid strep kits on Amazon. I have not seen them for sale in local pharmacies, but online ordering is simple and requires no medical license.
The Rapid Response Strep A Kit is one of the most affordable. The more elegant Quidel Quickvue is more costly, but perhaps a bit simpler for the layman. I have used them both. There are several other brands I have not tried, but as long as they are FDA approved, they should be fine.
Your doctor probably is unaware these kits can be purchased by non-professionals, and would be concerned about the accuracy of testing. Each test does come with a positive and negative control, which helps. I would consider a positive test as a true positive. A negative test may be due to operator error, or may be a true negative. Currently, physicians confirm a negative test with the more accurate culture (at least in children).
The kits have a shelf life of at least a year, and often longer. Would they be accurate a decade from now? My suspicion is yes, if stored under optimum conditions, though I cannot vouch for this.
Rapid strep testing is probably the best option for TEOTWAWKI. Strep throat cultures require additional expertise, storage, and interpretation.
When you purchase a kit, read ALL the fine print and experiment with a few test strips. You can learn this on your own (but we do cover home testing in detail in my Survival Medicine 101 workshop.)