There is no risk to your baby as long as your baby's carer does not have an open wound with bleeing and even then your baby would have to have a sore or open wound as well for any possibility of spread to happen. Your carer also is now on ARV treatment, but it sounds as if she has had an allergic reaction to her treatment. She must go back to the clinic so that she can be seen there and probably should be put on a different kind of ARV treatment.
It is unusual that your baby's ringworm keeps coming back. Apply Canesten cream [the original, not a generic] twice daily and hopefully this will clear up the problem.
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