Yes, you need a Mac, especially if you want to be able to use Xcode and Swift.

If you are short on money, you can try to buy a second hand iMac or a MacMini (just be sure it will support the next OS X version 10.10).

You do need to have a Mac to do dev, although you can go the Hackintosh route. I just built one using tonymac86's guide. There are a few gotchas, but it just basically works, and can be a good way to get started without buying something brand new.

I'm facing the same entry barrier. I am considering buying the hardware for it at this point

In my experience it's hard work without a mac.