My 6 month is allergic to carrots and sweet potatoes. Are there othere things I should be careful of? What alternatives can I give for same nutrients?

Plenty. Although both have high carotene content, neither is an essential food. Many yellow vegetables contains carotene. By the way, allergy to carrot and sweet potato is rare, even rare when allergic to both. Are you sure that your child is really allergic to these products? See an allergist if you are unclear about this subject.