I'm glad she laid her egg
Ok about the blue kote, was just wondering. If you have a picking problem there are a lot of articles and threads here on BYC and the web about the issue.
It can be cause by a number of things, from needing more protein to boredom or even just having an aggressive hen, that no matter what you do, she just can't seem to stop.
If the picking has created some small wounds or redness, the blue kote is a good camouflage and antiseptic, so it won't hurt and is a good product to have in your emergency kit.
Some people report good results with products like Pick-No-More, supposed to taste bad, but I haven't used it, so you might want to look into that.
Provide some boredom busters, hang fruit or veggies in the run. If it's nutritional upping protein content in the diet can help. Either use a higher protein commercial feed or offer hard boiled egg, tuna, mackerel or meat for a protein boost. Not having enough room can make them cranky so evaluation of space may be in order.
Just some ideas. Let me know how she is doing.
http://www.the-chicken-chick.com/2013/03/chicken-feather-loss-cannibalism-causes.html