My first instinct is to tell you to cut your losses and move on. At 4 months, you should not be fighting like this and overhearing him talk about you like that to someone else on the phone. Yes, guys will talk to their friends about everything in relationships, from the highs to the lows, so maybe he was just venting and honestly didn't think you could hear him. I'm not saying that's OK, because obviously it's hurtful, but it's not completely surprising that he would reach out to a friend.
Regarding the sex issue: guys definitely can have issues getting in the mood for sex when they are stressed out. It happens to every guy (and women, too), and some guys are more sensitive to stress than others, so it makes sense that it would happen more than once. The worst thing you can do when your boyfriend can't get in the mood, is get mad at him for it. Most guys get extremely embarrassed about it to begin with, and making them feel worse by making it about you is a pretty bad idea and would make any guy feel like sh*t. I know it makes you feel insecure and it can feel like rejection, but if you have a good relationship, it shouldn't be a big deal. If it happens again, hug your boyfriend, tell him it's OK and that you don't have to have sex to enjoy each other's company. That is a much better reaction than getting upset and starting a fight because truthfully, it's not a big deal, unless you are completely sexually incompatible and if that's the case, then break up.
At 4 months, you should still be in the honeymoon phase of your relationship, and if you want to have a healthy, happy, long-term relationship, you need to be able to talk to your partner about things that upset or frustrate you. If you want to work through this with him, talk to him about how you feel regarding his work commitments. Maybe suggest setting up weekly, or bi-weekly date nights so that you get to spend time together. If his working so much is becoming an issue for you, you need to talk to him about how you feel and try to come to a solution, otherwise the problems will continue and they will escalate.
Good luck!
"Caring is not an advantage."