How to heal a strained calf?

I have been exercising since this past summer, and recently have changed my bad eating habits and have a fairly healthy diet. About a month or so ago I started running. A little after a week I got up to running a solid mile without stopping, but then my calf started hurting and I couldn’t run! My dad said I probably strained it running these huge hills in my neighborhood. So I rested it for a week and iced it a few times. I continued strength training for the rest of my body. After maybe two weeks I did a cross-fit workout that involved burpees, mountain climbers, and jumping. I think those moves, especially jumping, irritated my calf and it hurt real bad the next day.

So it’s been four weeks since the injury and I haven’t gone running and have been real easy on it. It starts to hurt if I do any jumps or that sort and is tight and painful the next day. Besides resting it and icing it, what else can I do to speed the recovery and have a safe recovery? Also, how long should it take to heal?

I really appreciate any help.