You can use swoje / moje interchangebly, if it comes to person "I", for example:
Szukam mojego psa = Szukam swojego psa
But if it comes to persons "you, he, she and it", we use only swoje, for example:
On szuka swojego psa. (He's looking for his dog.)
Ona szuka swojego psa. (She's looking for her dog.)
Ono szuka swojego psa. (It is looking for its dog - that's a little bit strange ;)
Of course, you can say:
On szuka mojego psa
But it means , that he's looking for your dog, not his ;)
Hope you understand, and corrct me if I make mistake.