Hi dd2 is now 10mo and has been on nutramigen aa since she was about 7mo. The dietitian said about 2 weeks to notice a difference- if cows milk protein was the problem..
We did notice a huge difference but realised many other foods are also triggers. She has no dairy, soya, egg, wheat, banana, tomato, plum, melon..
As your ds is over 6 months you may have started weaning so go right back to basics baby rice, one puree at a time so you can identify other triggers.
Are you booked in for any allergy tests?
Be warned though the formula and diet on their own are unlikely to completely get rid of the excema. I skipped out of the dietitian's office hoping that would be the end of it. Her skin has majorly majorly cleared up, some days not even noticeable compared to broken red raw skin pre diet changes but she still itches and other factors like pollen, animals, wshing powder etc can be triggers.
Good luck. MN was my absolute saviour so many people on here with fab advice. HTH 