Peanuthead, they won't have been caused by rubbing her dummy in her eye. The meiboman gland in the eyelid produces oils that are used to keep the surface of the eyeball lubricated. There are hundreds of tiny little holes along the edge of the eyelid that secrete the oil. Chalazion are caused when some of the holes and associated ducts get blocked, causing an encapsulated cyst-like structure to form due to an inflammatory response.
My ds was three when he started getting them and we found the easiest way to get him to accept a compress was to get him to do it himself and then reward him.
One of the most common causes of chalazion (pronounced Kulazion btw) is blepharitis and the best way to deal with that is strict lid hygiene, such as the lid care wipes or lid-care kit or even regular bathing with boiled cooled water mixed with bicarbonate of soda.
I was very upset about the scarring, but he is outgrowing it now, so its not really all that noticeable and I expect it will diminish even more as he grows.
Ds was an extreme case in the early days, with chalazion cropping from one eye to the other and back again and each one getting severely infected every time. The consultant wrote to our GP stating that he should be prescribed cephalexin at the first sign of a lump and with that and the lid hygiene he had been lump free for 18 months until a few weeks ago. (He has recently been quite poorly, so I guess they returned because he was so run down.) We also have to call the hospital for an emergency eye clinic appointment as soon as one appears.
Fortunately, this time it hasn't been anywhere near as bad, but the blooming registrar we saw at the hospital had a go at me for getting him the antibiotics and told me he didn't need them because it was inflammatory not infected and chalazions don't need antibiotics unless cellulitis is involved. 
I then spoke to several other professionals in the same hospial clinic who agreed that she was wrong with regard to ds's case and her comments were based on someone with a very mild self-limiting chalazion, not a child with his history.
Anyway, I digress. I really hope your dd's eyes clear up quickly, please do try the lid hygiene and if they don't start improving very soon, go and ask for oral antibiotics. If her whole lid starts to look puffy, red and swollen, she is in any pain, complains of blurred vision, or any of them get really big, get her seen asap for oral abs, as 12 weeks is way too long to wait to get it sorted out.