Trust is very important in a relationship. Although you had known each other for about 2 years, you had gotten married recently. Perhaps he is feeling some anxiety since a marriage is a large commitment.
Texting or communicating with ex girlfriends and looking at their photographs is not appropriate. That is something singe men do;not those in a committed relationship.
How would he have felt if you were the one doing this with your ex boyfriends?
It is possible for counseling to help someone sort their issues, offer objective feedback and assist them in getting oriented in the right direction. The client has to want to make the needed changes in oneself though.
When you're dealing with an issue affecting the relationship, in addition to his own counseling, a couple's counseling will be most helpful.
The behavior is not appropriate for someone who is married or in a committed relationship. It seems that he wants to behave as though he is in an open relationship.
As far as whether or not he will act out on the behavior it will depend on his personality, honesty and morality level. It seems that you have a valid concern to suspect this possibility.