Ask your pediatrician if he/she objects to using sunscreen on your baby & if they can recommend a good one. (Disclosure: I've already asked my pediatrician about this because we're planning a family vacation to the beach in July. DD will be 4mos; I'm not staying inside all day!!)
You can also try a rashguard UPF rated for her arms; Target has their house-brand for $7.99. It's lightweight & wick-away.
Also, you my want to vary the times of day you're out & about, so you're not out during high UV times to try & minimize your exposure.
==========================================
Liz
DD (3/2010)
"Make mistakes! Get messy!" - Miss Frizzle