Interesting. I had a somewhat similar experience. Had all the symptoms and waited until my temp hit 102 before going to the ER.
They told me I had it. I said, "but you haven't tested me"? The ER physician said why test you? The results could come back negative and I still wouldn't believe it...at this point in time, everyone with your symptoms (including a 102 temperature) has it....why waste the test kit? He gave me a prescription for my cough and respiratory issues and told me to self-quarantine myself.
He did x-ray my chest though to make sure I did not have pneumonia, (Luckily I didn't) but he did not want to waste a test kit...which makes sense, either way, I was going to quarantine myself. He said 80% of the people who get it, are fine in a week or two. I am at day 4. If I don't post again.......I was part of the other 20%