Firstly, any file can be read unless it is still open by a particular process or service. Even PhotoShop files can be 'read' by NotePad - try it!
So, an attempt at my first answer...
You can try a couple of methods to prevent opening the file, for instance, applying a file lock. As an example, SQL Server .mdf
files are locked by the SQL Server service. This happens because the files are maintained in an open state, however; your application would have to remain running to keep these files open. Technically, though, the files can still be copied.
Another way is to set the hidden attribute for the file. This hides the file from the less savvy users, but it will be displayed if the user show's hidden files.
And my second answer: You refer to the format of files by saying only PhotoShop can read or write its own files (not true, but I know what you're saying).
The format of the file must be decided by yourself. You must determine how you are going to store the data that you output from your application. It looks like you have been attempting to write your application data into a text file. Perhaps you should try writing to binary files instead. Binary files, while not encrypted, as suggested by Visual Vincent in the comments to your question, still provide a more tailored approach to storing your data.
Binary files write raw binary data instead of humanised text. For instance, if you write an integer to the file it will appear as a string of four bytes, not your usual 123456789 textual format.
So, you really need to clarify what data you want to write to the file, decide on a set structure to your file (as you also have to be able to read it back in to your application) and then be able to write the information.