Simply put, text messaging is not secure. There are three issues:
As well as removing photos from your gallery, all patient data should be manually removed from the messaging app once sent and viewed by following these steps:
As stated above, if you're using an iPhone, SMS messages are being bundled together with iMessage messages. You should turn off iMessage if you wish to use SMS for sending patient data.
Of course, you can use a service like PicSafe where all data is encrypted and decrypted using a key acquired from a PicSafe Key Server.