In solo play, am I the player to my right?
Yes, you are the player to your right (and left) when playing solo.

From Devin Low, the designer of Legendary:


  Blackheart's effects say "The player on your right reveals a [MARVEL KNIGHTS] Hero or gains a Wound." When you do this effect in a two-player game, the other player is the player to your right, so that player must reveal or gain a Wound. In a solo game, the player to your right (going around the table) is yourself, so you gain a Wound.