@Superted No you are not being a princess! There should be some ground rules around the texting and photo sharing that take you into account.
To give him the benefit of the doubt... From his perspective he may be very nervous about the changes a new woman will mean to his relationship with his child. You may spend some extra time reassuring him before making any kind of request that affects the child. Just the fact that he took a year to introduce you to his child is telling of how protective he is of keeping the status quo. I understand taking it slow but a year is really slow. Usually by 6 months you know if your new paramour is a flight risk.
Keep in mind people do what they want to do. The battle cry of 'My child comes first' is a stance taken by many a single parent. While there is some truth to the fact that raising a child is all consuming. It is also used as a lazy way of putting off a confrontation he doesn't want to deal with. You say your relationship is only a year old. I'd heed this behavior as a red flag. It only gets worse from here. The fact that he was unwilling to listen to your concerns in a way that validated you is the real problem here. He may be still hoping something with his Ex Wife will pan out and is keeping you on a string. You really don't know for sure.
After the first couple of years of divorce people attempt to communicate with their Ex the same way they did during the marriage. They want to be friends, go on vacations together, etc. Or on the toxic side of things they want to argue, control and bicker like they did while they were married. Those parenting approaches leave little room for anyone new. The reality is if you want to include another person in your life you have to be willing to make room and negotiate an arrangement that works for all parties including kids.
Asking someone to put some boundaries around when they text a photo to an Ex is not unreasonable. As you get deeper into a relationship there will be a lot more demands made of you including parenting his child eventually. You might seek out some step parenting forums specifically. Read through the issues people face so you can see what's in store for you and if your love can weather the storms ahead. This forum has some good examples in the co-parenting section.
I'd ask the boyfriend for a serious heart to heart. Tell him how you feel. Be ready for him to break the relationship off or rage at you for wanting to explore the topic at all. Be ready to stand by your convictions and to walk away if you must. If he does either of those things it will hurt but it's better to know than not know. You can make an informed decision about where you stand in his life and whether or not you want to share it with him. You will respect yourself and he will also respect you if it works out.
All the Best and good luck!