Q: notes sync

If you updated your phone to iOS 9 and also updated to the new Notes features and you Mac is not updated to El Capitan (OS  10.11), that would explain the problem. See:

Before you upgrade your notes - Apple Support

The following may help OS X El Capitan - Technical Specifications

but you may also want to post a question about upgrading to El Capitan elsewhere on this forum (i.e., outside of the "Using iPhone" section) to get some input from  someone with more knowledge in that area.

Another option you may want to consider, especially if you do not want to upgrade your Mac to El Capitan, would be to switch from Apple Notes to Evernote on both your Mac and your iPhone. I use Evernote and prefer it and the free version is vey capable.