almost all antibiotics have some activity for bartonella
none to my knowledge are super specific
the studies from Zhang et al tend to show even those not typically used for bartonella - like cephalosporins - kill around 30% of viable bartonella cells in the lab - while more commonly used drugs like doxycycline tend to kill around 40% - so there's not a lot in it - which is no real surprise as all of these drugs were designed to be broad spectrum in action
of course there may well be differences in susceptibility from strain to strain also.
to arrive at some kind of differential activity - it would also depend on what organism is causing the sinusitis - and what that's susceptible to - which may well be unknown - unless its been swabbed and cultured
another option may be to try something topical - like an antimicrobial nasal spray for the sinusitis
edit to add link to Zhang's FDA drugs screening paper
https://www.ncbi.nlm.nih.gov/pmc/articles/pmc6628006/hope its of some help