Without getting into the specifics of your experience I just want to say that letting an occasional embarrassment prevent you from continuing something you enjoy is something you may regret later.
Most coaches do not like being backtalked. It sounds like you were really frustrated, but your coach may respond better to statements such as "I'm trying my best" or "I'm getting frustrated" or "I'm struggling with this, should I just do as many as I can correctly?" or silence.
In regards to the embarrassment just walk in there with your head held high, no one can make you feel bad but you. If your coach or teammates comment on the situation just say "yeah, I was really frustrated but I feel better now" and leave it at that. All people have embarrassing situation, including coaches! We all do and say things we wish we could take back. Apologize if you feel it is appropriate or necessary to preserve the relationship with your coach and then forget about it and move on.