What I'm wondering is what would you and your friend be trying to "win" from this relationship? You say that you are competitive with her but not exactly how you see this competition playing out. Would you be looking at ranking time (which can be doled out evenly) or looking at ranking emotions (which are extremely difficult to quantify)? Could you look at your relationship with your partner as separate from her relationship with your partner? Your partner is with you for a reason, as long as your partner still choose you it really shouldn't matter WHO else they are choosing.
Everything will be ok in the end. If it's not ok it's not the end.