Not normal, and I would suspect it's a boot issue - either the wrong size (too long, too short, too narrow, or too wide - lots of possibilities there), or you are lacking the necessary support in the footbed for your feet. Even with boots the correct size, I can't skate without extra arch support in my boots or my feet will cramp up like crazy... so bad I can't be on the ice for more than about 5 minutes. With my arches properly supported I am fine though. I don't have orthotics in mine, just arch cookies (and post wedges under my heels, but that's for alignment, not pain)... but the important thing is that they provide the support that my feet need.
Numbness and swelling is definitely not normal though... it is your body trying to tell you something is wrong.
You really need to get fitted properly, and I know you have posted that there is nowhere local to have this done, but TRUST ME, it's not worth the potential damage you can do to your feet by pushing through it with boots that do not fit right. I ended up having surgery to fix an ankle problem created by one pair of boots I had (they were much too narrow) - and before it got really bad, I had just assumed it was normal, had the ankles and toebox punched out, and pushed through it, and that was a huge mistake. If we'd just spent the money on another pair of new boots or demanded that the fitter replace them with the size I really needed, we would have ultimately saved thousands on surgery plus additional pain and time off the ice.