You weren't on it long enough - when you stop treatment too soon, the symptoms come back.
How long did you have symptoms before you started treatment? Is this a recent infection..or chronic?
You could show him Dr. Burrascano Lyme Treatment Guidelines - ILADS has a link to them on their site.
the guidelines show the dosage of doxy, as well as duration of treatment depending on the stage you're at.
If you've had symptoms for many months (and disseminated) - you are looking at months (or longer) not weeks of antibiotics.
www.lymenet.org/BurrGuide200810.pdfPage 18 - dosage of abx
Page 19 - treatment categories.
You can print off those pages for your Dr.