If it were me I would say something like "I have sent a letter/picture before and just wanted to make sure it didn't get lost in the mail"
I think it is ok to write again once just not multiple times.
Keep in mind many people have waited over a year and there Is still a chance to get a response.
Many people do not respond to every letter it may be wise to include a picture.
That's just my opinion

Hello! If you’ve waited a while for a response from a celebrity is it ok to write again? Especially if you didn’t send a pic to sign, and this time send a pic? Or could we write again and try a different address?