There are some (rare) bullhorn shaped bars with the right dimensions, typically sold as integrated bar end mtb bars (but many bars sold as such are thinner toward the front).
Many bar ends are 22.2mm if you don't mind your bullhorns not being one piece.
I don't think I would care for that myself, but bar ends are cheap if you want to try it out.
If you haven't used drops you should try them out. At least ride one of the road bikes at your LBS. Better yet barrow or rent one that you can ride for a couple days.
Drops may or may not suit you, and would call for either a new bike or a fair amount of new equipment.
You're the only one who can decide if drop bars, brifters, and the whole shabang are right for you.
Bar ends and alternative handlebars compatible with your current components will be cheaper, and in this case I'd say it won't hurt anything to experiment.