If you will continue applying Coconut oil, it will block the pores in skin of your baby from where sweat comes, causing eruptions as described by you, so stop it at the earliest. As for soaps, its best if no soaps are used in babies because of this allergy
Its best to bath baby with plain water and then clean dry with a cotton towel. If soap has to be used at all, use low pH ones like Teddybar. Thanks.