This could be heat rashes or just baby skin going through some changes as they are less than a month old. Meantime, dont use thick clothes and just use cooling attire. Dont put moisturiser or powder but perhaps you can try kodomo lotion powder which may help in the meantime. If it is allergic, baby would develop a very bad rash or feeling the symptoms of allergy. While if it is eczema, it will be extremely dry, flaky skin.
looks like heat rash to me.