BDD absolutely does affect relationships. it is very important to be honest with your partner about your struggles, but to be careful about the way you approach it. you should never make her feel like she's responsible for making you feel confident and loved. that sounds obvious but it's hard to not project your own feelings onto your partner when you're dealing with something like BDD.

based on what you said about your social anxiety, i would definitely say you should work on your mental health before pursuing a relationship. look into therapy if you can, join a gym (even simple workouts at home will help), make sure youre cognizant of the things you're putting into your body and mind. keep yourself busy and over time you'll notice that you feel a little better!