I've captured some Great Prophets, now what?

One thing to keep in mind is that any major religion is superior to no religion at all. Yes, it gives a bonus to your opponent, but it gives a larger bonus to your city. Therefore, its advisable to use these GPs to spread religion to cities that do not have, and are unlikely to get, Shinto. Island colonies far from other cities are the best example. They would not otherwise get a religion, so it can be wise to spread buddhism or confucianism there.

Finally, look at the benefits provided by those religions. If you have a specialty city, it may be useful to add a specialty religion. For example, if you have a pure production city, and Buddhism gives the 15 percent production bonus, it may be wise to spread Buddhism there in order to get said bonus.

Great Prophets can be expended to construct the "Holy Site" tile improvement, which can be worked for faith.

Faith is agnostic, so it doesn't matter what religious flavor of prophet constructs the tile improvement. Since only two non-faith-purchased buildings produce faith (shrine + temple), you may find the smattering of extra faith useful.

A great use of Great Prophets, which can only be taken advantage of by Sweden, is gifting them to city-states to gain 90 influence. This can be incredibly helpful when you have a particularly aggressive enemy who sends great prophets in droves.

As other said, sometimes their religion can be usefull for some city. Eg. if it allows religious building and you are generating enough faith, you could convert some of your cities, build that building and reconvert back (if done in middle of your religion, one city will be converted relatively quickly).

Another use is: You are pushing your religion against another and gain GP from third. You can now convert some of their cities to that third religion, thus removing part of their preassure while keeping yours.