Based on your description it appears that you have FileVault enabled. Therefore the fact that you can't select your main OS X partition by holding option or X key is completely expected — it's encrypted, after all, and the EFI firmware does not know anything about FileVault.
The normal boot sequence with FileVault enabled is like this: EFI -> Recovery HD -> OS X.
In your case, something on your recovery partition got corrupted, that's why you can't boot.
WARNING: since your drive is encrypted, make sure that you have current backups of your data before doing anything. Especially steer clear from Disk Management in Windows, I have seen it change the partition type on several HFS+ disks just by opening it.
Also, booting internet recovery can be very time consuming depending on your internet connection. If you have a Time Machine backup, you can boot into recovery from it by holding down the option key at boot. If not, I recommend you boot into internet recovery and install OS X on a spare USB drive (can be external hard drive or a flash USB stick ≥8 GB). It won't affect your internal drive and will make the recovery process much easier.
I can think of 3 possible scenarios (from easiest to repair to most difficult):
- Windows Disk Management, as it is wont to do, changed the partition type of your Recovery HD from Apple_Boot to Apple_HFS.
- Difficulty: easy
- How to detect:
- boot into recovery mode, open Terminal and type this command:
-
- look for the partition type of Recovery HD (disk0s3): if it is anything except Apple_Boot, then you have this problem.
- How to fix:
- while still in Terminal in recovery mode, type this command:
-
Code:
asr adjust --target /dev/disk0s3 --settype Apple_Boot
- Boot caches on recovery partition got corrupted
- Difficulty: easy
- How to detect:
- If the partition type of Recovery HD, as determined in case 1 above, is already Apple_Boot, but the system refuses to boot into OS X normally, you probably have this problem
- How to fix:
- open Disk Utility in recovery mode, then unlock and mount your internal drive
- quit Disk Utility, open Terminal and type this command (assuming your main partition is called "Macintosh HD"):
-
Code:
kextcache -u /Volumes/Macintosh\ HD
- Recovery partition is damaged or missing completely
- Difficulty: difficult and time consuming (several hours)
- How to detect:
- If the solution in case 2 above doesn't work,
- or there's no Recovery HD on disk0 at all, then you probably have this problem
- How to fix:
- The most reliable method is probably to backup most important data and reinstall OS X.
- The more involved and error-prone method is to download OS X installer from Mac App Store and then use the dmtest command from "Recovery HD Update" package to recreate Recovery HD partition.
In my experience with Windows 10, I had a similar problem — Disk Management silently changed the partition type of Recovery HD. It was very easy to fix (see case 1 above), however my drive was not encrypted. In your case, FileVault complicates things because if something goes wrong, there's a risk to lose all your data.
