As someone who has had multiple professional piercings over the years and has had to deal with an infection here & there (I had one piercing that acted up every single time I got a cold, without fail), this is my advice, taken straight from professional piercers who are trained in this kind of stuff:
1.) Do NOT take the jewelry out. That's just going to seal the infection in the healing piercing. Leave the jewelry in. If it's crappy quality & that's what you think is bothering her, then remove it if you can & replace them with higher quality earrings, but do not take them out & leave them out.
2.) Do NOT use alcohol. It's too harsh. Clean with a gentle antibacterial soap and soak it in a warm sea salt solution (1c warm water + 1/4tsp non-iodized sea salt). Clean the piercing once a day, but you can do the sea salt soaks as frequently as you'd like. It soothes the piercing, loosens up an crusties & is a natural astringent so it draws the infection out. You can have her stick her ear in a cup of the solution or use a cotton ball to gently hold it against her ear. Leave it soak for several minutes.
3.) There is no need to spin the earring. Unless you want to make your kid cry, in which case, be my guest!

Seriously though, it doesn't do any good at all & just inflicts pain
Hope it heals up quickly! These things will happen time to time with piercings, especially with kids, but definitely keeping her from wearing cheapo jewelry will help. If she does want to wear the cheap, cute stuff, that's fine, just limit it to a couple of hours.