Hello. Thanks for writing to us at healthcaremagic Peeling is quite normal after a sunburn; the sunburnt skin will ultimately peel off revealing a light pink colored new skin. Bland moisturizers are all that are recommended during this period, therefore in my view you should stick to just moisturisation. Neosporin is a topical antibacterial and it is really not required. Moreover neosporin is quite a common sensitizer and a very common cause of allergic contact dermatitis (ACD). Therefor, it is advisable to avoid it where it is actually not needed and better not risk another problem i.e ACD to neosporin.. Regards