Currently there is no way to check it in-game, but thats a cool idea that I'll implement in the upcoming version :)
Hopefully this week I'll be able to post a video preview of what's coming soon :)
Are there some you can only get on certain difficulties? I only play on Challenge, and apparently one of the ones I've been missing is the eye, which I start out with.
That's a bug, if you start with a relic it should be unlocked automatically. It's already addressed for the next release :)