Hi Cheryl, the best thing for you to do, beings g.p. doctors do not treat Lyme and co-infections with the proper protocol. Is to seek out a LLMD, (Lyme Literate Medical Doctor).
Your right , 3 weeks of antibiotics is not long enough. There are 3 life stages to the bacteria, so it needs to be treated with more than one type of antibiotic. Then there are over 300 different strains of Lyme, and the labs don't test for all of those. Same with co's such as babesia, there are different strains. So it is hard to detect what strains we have.
There is a thread above how to Share LLD names. And from where you are sitting, you might be able to find a Lyme support group in your area, city, county, or state. There may be a contact name that you can request a LLMD name. Many do not take insurance, so it will be a out of pocket expense.
I hope you find your answers soon, and get on the right treatment.