If you're using Globe then that means your phone is now unlocked, right? Otherwise, there's no way you can use Globe with that. So you shouldn't base it with Verizon's schedule. Check your phone's region in Extras+info. If Cyan is already released in whatever region indicated, then you should be able to update to WP8.1 with Cyan. For unlocked phones, he update is based on the phone's region.
Personal experience: I'm from the Philippines too, with Sun Cellular as my carrier. I couldn't get Cyan/WP8.1 even when it was officially released here. Then I found out that my phone is actually Hong Kong variant. Waited a little while longer to get it.
If you really can't wait any longer then download and install Preview for Developers, enroll in it and check for updates. Be warned that using the DP will only give you WP8.1 and not Cyan. You may (and you probably will) encounter bugs with this. Also, if you decide to do this and Cyan gets released for your phone, you can't simply download it. You will have to reinstall WP8.1 with Cyan via Nokia Software Recovery Tool. That erases your phone's personal content (you can back up though), so it's a hassle.