You can purchase and probably find free programs which allow editing of PDF's. If you don't want to purchase anything and can't find a freebie, there are several pdf2jpg websites that will convert your PDF's to JPG's then pull your JPG files into PAINT in MSWIN and use a music font to add notes or even text. This is much easier than your Photoshop method. Then, use a JPG2PDF website to convert it back. That is the long way but it works. Alternatively . . .
I have used free PDF editors in the past but don't remember what they were. Now I convert everything to JPG because they are much easier to use and manipulate. There are a dozen music fonts out there for free.
Just do a Google search for "free PDF editor" and you'll find them or you'll see several websites that will do it for you. I prefer websites because there is nothing to download or install. So what if they are peeking up my skirt, I don't care.