Yes, I believe you need a Mac. I also wanted to program for iOS using my PC, but I remember looking extensively until I found an Apple website basically saying that you need to have a Mac.
You can write your header and cpp files in any editor, but for compiling and sending an app for revision to Apple you still have to use a Mac. In fact, I believe you do have to use Xcode as well.
iMac Book Pro, MacOS 10.12.4, Xcode 9.0.1;
iPhone 6, iOS 9.35; iPhone 5s, iOS 9.35; iPad (3rd gen), iOS 9.35;
Dell Precision T7400, Windows 7 Professional 64bit, Visual Studio Community 2017;