A week of recovery is not unusual for recovery if your zapping is done correctly (mainly, you should never feel like the hairs being extracted are in any way being plucked).
To kill the hair, the stem cells of the hair follicle have to be destroyed, along with the blood supply. This in turn causes the body to react, triggering a healing cycle for the skin. Skin doesn't heal overnight. Blood and plasma will fill the emptied follicle, and phagocytes will rush to the area to start eating up debris and any potential microbes that have been introduced to this sensitive area. The nice thing, though, is that your skin will actually be creating new collagen...
Back in the day, I was getting at least 4 hours a week of blend, and sometimes 8 in two sessions, covering different areas just to get clear. I'd take plenty of acetaminophen or ibuprofen for pain relief. The redness at such a pace would last a few hours, up to a day for heavily concentrated areas like my upper lip. Swelling for 2 to 3 days. The treated follicles would be little pinpoints of red and swelling for up to a week. Today I'm regularly pegged for being about ten years younger than I actually am (though the estrogen certainly helped with that as well).
Good aftercare can facilitate the healing process. Immediately after a session, treat gently with ice or coldpacks for about an hour. I always liked to apply a layer of pure aloe gel, keeping it on until bedtime -- the aloe acts as a barrier to keep microbes from getting into the open follicles. For daily face cleansing, use something gentle (a "sensitive skin" product), rinse, then apply witch hazel, which acts as a astringent to close up the pores, again helping to prevent infection (witch hazel isn't nearly as harsh as most astringents or toners). Finish with a mild moisturizer -- you don't want your skin drying out.
Finally, operator skill is absolutely key. Someone with a natural talent and understanding of the process (who is trained by someone reliable) can be very good even with only six months of experience. Conversely, there are electrologists who've been out there for decades that I would never let touch my face, moreso because they can be ineffective (sucking up your money), though of course there are some who are too aggressive with their thermolysis and can cause lasting damage.