Glad to hear it is responding well. The antibiotics are preventive only because the wasp may have had bacteria on its stinger and that has penetrated the protective outer layer of skin.
Cold packs don't stop swelling from occurring but they slow it down and can considerably reduce the amount of swelling. That, in turn, reduces the recovery time. Injuries can continue to swell for a couple of days, which is why they recommend use cold packs for the first 48 hours only. After that the use of warm packs helps tissues mend. I've had a few Phy Ed classes in my time as a teacher, so had to learn all the first aid stuff.
Now to my learning experience at an early age. I was sitting on the grass strip between the concrete paths of the driveway, when this beautifully coloured fly landed on the patchy kikuyu grass about a metre away. It flitted around like it was looking for something and suddenly went down a hole. Wanting to observe more I put my hand over the hole to keep it in. I then looked around and spotted my sister having atea party on the front with their dolls. So I yelled out to my twin to bring me one of the cups. Well Mum was just coming out front door to call us in for lunch as my twin handed me the cup. At the same time I let out one almighty bellow, jumped to my feet and did my best imitation of an Indian Rain Dance with tear streaming down my face and one hand firmly wrapped around the wrist of the other as I shook it up down in front of me. My sister looked at me, turned around to see Mum and immediately burst into tears blubbering something about how she didn’t do it, while at the same time wanting offer to offer me comfort, but afraid that she might incriminate in so doing. So she burst into tears and started to lose it.
Poor old Mum didn’t know what to make of it. Should she be chastising someone for doing something to some else, although she had no idea what. Or should she be offering solace to her upset little twins. The trials and tribulations of being a parent. As for me, I very quickly learned the difference between wasps and flies and never made the same mistake again.
As for the paper wasps, I did once accidentally disturb a nest in a bush. I heard the collective drone of dozens of wings beating and would have given Usane Bolt a run for his money given the rate I hightailed it out of there. Remarkably, I got off scott free. Not one sting.
Like Scutellatus, I used to get them inside the shed. I could go in and out and they never worried about me. A few times they started to construct their nests below the door aperture, which was a little too close to me head for comfort. O having an understanding of their ecology, I sprayed the nest several time a day for several days with a water bottle. Sure enough, they decided they had built in the wrong place and abandoned that construction. I probably did that half a dozen times in 25 years.