Yeah, I have this problem - I get gassed really fast. How can I improve this? Currently, I can't afford to go to gym, so I can't use any equipment. I have a really crappy boxing bag at home, but it's better than nothing. So I guess that shadow fighting and using the boxing bag are going to help with this problem, right?
I also suspect that it could be because I'm not relaxed enough while hitting.
Right and right. The best way to train for standup is to punch and kick. The best way to train for grappling is to roll. And they don't really translate to each other very well. I mean, you can be in great shape for one and suck at the other.
wind sprints and hill/stair climbing will help more than paced running. Also circuit training where you go from squats to pushups to pullups with no rest in between can help.
anything that get's your body used to dealing with large buildup of lactic acid helps.
Swimming underwater holding my breath helped me a lot but, there really is no substitute for sparring and rolling.