After finishing chlamydia treatment of doxycycline, can i get retested without a false positive 1-2 weeks after?

Too soon: Retesting probably isn't necessary at all. Doxycycline never fails to cure chlamydia, if taken as directed (usually 2x daily for 7 days). But if you would feel better with a repeat negative test, wait until 3 weeks. Earlier tests can be false positive, because chlamydial DNA persists for up to 3 weeks after cure. It's more important to be retested after 3-6 months, because reinfection is common.