First off, thank you all everybody for your support. I was really upset initially more so because the big fan I am of home remedies, it meant that I would have to toughen up and get immune to her cries for them to work . And yes I managed to do both... time, patience & a stone of heart. Damn why did parenting have to be so hard! now that will make for a totally different post...
So here is what I did..
For the Cyst in her eye: Rinsing eyes with Meethi Seeds decoction is a good remedy for all eye related problems. rinsing the eyes of a toddler, was tough. After a lot of debate, using it as eye drops was the best. And after a lot of trial and error, its best to use it when the are asleep! Just pull down the lower eye lid, and voila its done. No cries. No pleadings nothing.
For her ears: Turns out that the supposed gold plated earring was made of inferior quality material and hence the infection was going bad to worse. So it was Kari pata (fresh) to the rescue. The stems have medicinal properties. Seeing is believing they say and within 6 hours there was a noticeable difference. And in 24 hours, I could actually see her pierced ear lobes without any pus or blood. The sticks would turn black, it was as though it was pulling/sucking all infection into itself. The sticks have to be replaced everyday, they shrink in size and dry out. Neem sticks cannot be used, since they rot the ears, making it a whole lot worse.
The whole operation, was done when she was sleeping. Removing, cleaning & oiling. Used Entrops on the ear lobe and the sticks too. The cyst took about a week to clear more so because, I could put those drops only during the afternoon and though her ears look ok now, have been advised to keep it going for another month.
The worst, she has sworn off earrings. She does not want to wear them. Period. Even though her ears don't pain now, I'm still not allowed to change the sticks when she is awake. I'm planning to take her to the jeweler, to shop for her new earrings, hopefully then she'd be interested again. And yes she has also become very alert during her sleep. If she feels any pain and is woken up, she looks every few minutes to see if I am in the room or not and so I am not supposed to be sleeping next to her, if I touch her eye or ear.