What could cause a hangover feeling without drinking alcohol?

Possible migraine: or sinus issues. Please see your doc for proper diagnosis. Peace and good health.

Use of other drugs: One can feel hung over after using many drugs other than alcohol -- including sedatives, anti-anxiety agents, and anti-psychotics; even some antidepressants. Some of these may have been prescribed for you -- in which case please consult your physician about dose adjustments or medication changes. If you're using substances acquired illegally, then it's impossible to know what's in them.