First and foremost, there is nothing wrong with having a healthy, happy relationship based on the D/s dynamic.
Note that I said "healthy" AND "happy". In order to have both, the Dom and the sub have to be at a point in the relationship where the Dom is able to care properly for their sub's needs and ensures that the level of play remains at an appropriate level of care and kink at the same time. Their sub will need to know and trust that the Dom will always have their safety (and sanity) first and foremost throughout the scene.
Also note that not all D/s partnerships need or require a safeword. It is possible to have a perfectly safe D/s relationship or scene where no safeword is needed - *provided that the Dom and sub know each others hard limits extremely well, and that both partners are completely able to read each other well*. That way, if the sub is in distress, or something just doesn't "feel right" for them, the capable, caring Dom will sense that. They will either end play immediately, or reassess the situation and ensure (by talking to the sub) that they change whatever it is that's being done so that both partners are content and secure.
Again, safe words are *NOT* an absolute requirement, but they do help keep things from getting out of control. My girl has a safeword (and she's used it a few times during our scenes), but hasn't always had time to use them. I can think of at least one time where I accidentally hurt her, and she didn't have the opportunity to safeword. I sensed that something was wrong, and we stopped immediately, while we talked about the moment, and I ensured that she was ok. By showing such care for her, it allowed her to relax so that she requested that we continue where we had left off.
Unfortunately, that does not seem to be the case here. Your boyfriend's lack of empathy for his submissive is particularly worrisome. A Dom *must* care for their sub, even if only a little (although, let's be honest, more is better), else the wellbeing of their sub is at risk.
You're claustrophobic. That's a hard limit, unless you've told him you are interested (and able) to push that limit a bit. If you're not, and he doesn't seem to recognize that (or care), then this is probably a good sign that you need to walk away from this, and him, right away. If you don't, the likelihood that he will hurt you worse, later, is almost inevitable. Find a guy with your level of kink, and who is able to recognize (and respect) your needs and your limits.