HI J.,
I have a 4 1/2 month old, and I'm sorry but I don't have a suggestion for the bug spray except for using a net over your daughter's bouncy seat or pack n play to protect her from the mosquitos.
But, I can help you with the sunscreen issue. I market a plant based product line for parents of children who have very sensitive, itchy, dry skin. In the product line is a sunscreen for babies that is SPF 30+.
The bottle suggests for babies younger than 6 months to ask a doctor. I would recommend you do the same, but my pediatrician said it would probably be ok. I used it last weekend when we went to Ohio to visit family and my son did just fine with it.
I'd be happy to send you a sample of it or send you a full size bottle of it priority mail today...you'd get it in tomorrow's mail. The sample is free, but won't get you through the weekend. The bottle costs $22 plus $4.80 in shipping, so a total of $26.80.
The company does offer a wholesale membership if you're interested in receiving a 35% discount, but I'd personally recommend you try it to make sure you like it before you do that.
Let me know if you want it and I'll get it in today's mail...please feel free to email me or call me if you'd prefer. ###-###-####