First of all, whoever pierced your ears with studs that were too short needs to be reported to the health department. This could have caused major damage to your ears, even more than what it already caused. It could happen to someone else. When you get your ears pierced, the posts are longer than normal for a reason -- to allow room for swelling. Since your ears probably did not have room to swell, your ears actually swelled around the earrings. I'm glad you got them removed and will be okay.
Even though the infection will be healed up in about a week, you need to make sure the piercings themselves are healed up fully before you get them re-done. Without jewelry in them, lobes can heal in 2 months, sometimes sooner depending on the person -- however, to ensure they are fully healed, wait about 3 months before getting them re-pierced. You definitely do not want to add new problems onto existing problems.
Just a quick FYI -- if you develop significant scarring on the lobes, you may not want to get them re-pierced. Piercing them again with scarring present can make the scarring grow larger, which i'm sure you do not want on your ears. If the scarring is big enough, it will be hard to find someone that will re-pierce them in the first place.
As charlotte said, go to a professional piercer. The results are far better than what you would get after being pierced with a piercing gun. Piercing guns can cause minor to moderate damage to your ears, and they arent worth the hassle to save a few bucks.
Good luck!
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