So there's an ice shard stuck in my character. Have many other people had this or similar? I hope it'll go away if I get hit with ice shard again, or do something else soon.

It will go away eventually. I ran around with an arrow stuck in my head and an ice shard in my body for a good 20 minutes. I didn't pay attention to what got rid of it, but you might try sleeping or waiting it out.

Once you exit the game, it will be gone next time you play.

play in first person so it wont bother you.... hur dur dur