Prednisone works quite well to stop attacks for many people, but for most people that's only during the time that it's being taken, or even, for many, only during the time when the higher doses are taken. Some people find that if/when the attacks come back, they can be quite severe. The recommended prednisone dosage for CH is 1 mg/Kg up to 60 mg for four days tapering the dose over three weeks. If your cycle typically lasts a month and you get up to three weeks of relief, that seems possibly worth doing. Some people also get relief from the standard prednisone "dose pack," which is shorter.
I don't think Emgality would be contraindicated with prednisone, but I don't really know. Reports here about Emgality are mixed, as snafu says, but you have to keep in mind that not many people are going to show up here reporting on something that worked for them. You can see comments about Emgality by putting the word Emgality into the search bar at the top right of any page.