Will periorbital cellulitis stop me from going on my vacation?

Yes: Get it treated before it goes into your eye and affect your vision. Or spread to cause meningitis.

Severity?: Preseptal cellulitis can potentially resolve with oral antibiotics. Postseptal cellulitis may need IV antibiotics. Any eye movement disturbance is worrisome and usually involves imaging. Amount of swelling and spread can be factors. Also if not improving on first line therapy, that would stop vacation. So depends on severity, length of time, treatment working or not, etc.