I am currently stuck in Spain, having contracted COVID-19 and missed my flight to the US. I've been in quarantine over a week, I feel fine, and I can legally go out in public according to both Spanish and US public health guidance. Howe, I keep testing positive on at-home rapid tests, so I can't reenter the US.
One possibility that has been suggested to me is to obtain a certificate of recovery instead of trying to get a negative test. This requires an official (ie, not at-home) positive test and a signed doctor's letter indicating recovery. The doctor's letter I should be able to get through either a telehealth visit with my PCP or an online service. However, I do not currently have an official positive test, because I've just been taking at home ones the whole time I've been in quarantine.
If I get a signed recovery letter and an official positive test on the same day, say tomorrow, can I use them together to fly the following day or two? The CDC airline guidance doesn't appear to prohibit this- it just lays out requirements for the type of test and says it needs to be administered in the last 90 days. However, I would've assumed the positive test would have needed to be at least 10 days old or something like that to prevent currently positive travelers from flying, so I want to double check. Will this work?
Edit and update: based on doc's answer and a conversation with my doctor, I agree that I shouldn't fly until I start testing negative.
However, the question still stands: I now have an 'official' positive test as of this morning, and my doctor has agreed to write me a recovery letter once I get a negative on at at home test. So, suppose I test negative at home tomorrow or Sunday, and get the letter from my doctor. Can I then use these documents to fly, or will it be a problem that the positive test is only a few days old?
Obviously the safest thing to do is to get another official test, but I'm currently in a small town in Spain where such tests are expensive and difficult to schedule, so flying with the recovery documents is preferable if it will work.
Update & bounty: I now have a 2 day old official positive test, a negative at-home test as of this morning, and a doctor's letter indicating that I am no longer contagious. The question remains whether I will be able to successfully board a flight in the next few days with just these two documents, or whether I need to get another official test (which is expensive and inconvenient, but doable if necessary).