YES YES YES YES YES YES YES YES YES YES YES YES YES!!!!
ALWAYS try to test the tick for as much 'stuff' as the testing place will agree to.
Here are a few places - not sure where you live:
UMass has a tick testing program:
/ag.umass.edu/services/tick-borne-disease-diagnostics
/www.tickreport.com/Says it provides results w/in 3 days!
Bay Area Lyme
www.bayarealyme.org/lyme-disease-prevention/tick-testing/IGeneX
www.igenex.com/wp-content/uploads/2016/12/BS-F-036-TICK-TEST-REQUEST-FORM-REV.002-11-11-16.pdf-p