Designing Kitchens and Bathrooms - Tile on shower alcove ceiling?

My home was built in 1928 and has white 4-inch square tile about 2/3 up from the floor, throught the entire bathroom including the tub enclosure. A black border is at the bottom and top.

At some point, the prior owner added a shower head. Unfortunately, now all the paint is peeling off the shower walls and ceilings (all plaster walls).

Can I apply tile to the plaster or should I repaint?

Thanks.

Personally, I would repaint.... You're gonna have a heck of a time finding matching tile - matching patterns, matching grout - it's gonna look patched...

More importantly, you've got a questionable "base" for thinset, grout and tile at this point. That paint is peeling for a reason..... either the plaster is wet and the bond separating or the paint is cheap and wouldn't stick anyway.... not to mention it's old, old, old....

Scrape off the old paint thoroughly.... apply a good sealer/primer to the plaster followed by a top quality latex enamel.

How high up is the tile?

I would opt for tile, but as thezster mentioned, it might not be as easy as just putting it up.
might require some demolition and repair of the walls.

You may have latex paint on top of an oil base.

scrape good
then prime and paint with quality paints. I'll second that.