Fight Help

So, I'm really (really) new to the entire boxing thing. However, for now, me and a friend of mine bought some gloves and some of these padded gloves you can punch (or work on drills). Originally, the idea was to be like the movie "Fight Club," however, as time has gone on over the last 3 weeks, it's now more like boxing than anything else, in fact, it's completely boxing. Generally we meet a couple times a week and at first go over a few drills to work on footwork, and then punch the mits (I don't know what to call them). Then we fight a few rounds which last until someone gives up. This will sound pathetic, but this is the first fighting experience I have had period. I get hit in the nose (this is the second fight in a row as it get a little more intense every time) and it bleeds and stuff. I mean, yeah it hurts, but not that bad. Do I need to let it heal a while before the next fight? Can I really mess up my nose if I don't let it "rest" or "rejuvinate?" Is the whole idea of fighting like this ridiculous? I guess I have a lot of questions eh?