Why can't I load my saved game in My Boy Free?

Solution 1:

The only way for you to actually get those saves is through buying the premium version.

So your progress is basically gone until now. However you can save from the game itself, not the emulator. I play Pokemon on the emulator myself and the only way to save is through "start > save". It will mostly not influence your game until you get to some bosses where having on the spot saving makes it easier.

Solution 2:

You have to save from the start-menu of the game, not from the emulator's menu.

If you're afraid you've lost some progress, you can load the savedata from whichever (as far as I know) emulator, so if you get the Premium version now, you could load back what you saved in the Free version.