Some allergic reactions to sunscreens in children may be caused by para amino benzoic acid (PABA), so you need to get one that is "PABA" free.
I would get one that is 45 SPF or greater and put sunscreen on 20 to 30 minutes before going outside.So many people make a mistake and put it on when they are already outside and think they have instant coverage. You should really put in on every two hours as well.
I am a total freak about this. Having bad sunburns in childhood predisposes some people to skin cancer later in life....being my father had some areas removed due to cancer, well lets just say I have sunblock everywhere accessible!!!!!!! Car, stroller, diaperbag, in the garage etc. A lot of ped offices get samples from reps so you might want to check your dr's office and see if they have anything you could try.
My daughter still has a touch of baby ezcema and we use "Blue Lizard" baby sun block and it is the only kind that doesn't make her breakout more. Hope some of this is helpful