Mayyyybe... But the way it erupts outward from the tonsillary area isn't really characteristic of papillomae.

I'm not about to play Internet diagnostician, of course, but it's either a funny-looking tonsillolith or a very unusual presentation of a papilloma.

My money in Vegas, though, would be on the tonsillolith, just because of the location and "erupted" look.

But either way, doctor. Even tonsilloliths, while basically harmless in situ, can be dangerous (and painful!) to remove, since you don't know what kind of formation can be hiding beneath. Some of those suckers have massive bases, with just the "tip of the iceberg" visible.

Also, note the "bumps" above the left (his right) tonsil. Looks like additional, un-erupted 'liths are hiding up there.