I have had the very same problem. I could not send pictures to my husband or son. I could not send group messages either. I went to the Genius Bar and they told me that I had a software issue and I should backup my phone, restore it to original settings, then back up the phone. Did not work. Genius Bar then said that I didn't do it right, I should back it up, restore it to original settings, then sync each setting, not to back it up, because I would just be putting the problem back on the phone. Did not work. Genius Bar said I needed a new Sim card. Did not work. They did not know what the problem was and gave me a new phone. SAME PROBLEM!!!
My other son then asked me to send a photo to my husband. I started to type his address into the To: line and he told me no, I should use the + in the blue circle. He then asked me to send a group message. I started to do the same thing and he again told me to use the + in the blue circle. This took care of my problems.
No where are we told to use the +sign in the blue circle. Apparently there is some sort of connection that is made when you do this. Please try it and let me know if this helps.