Am I obligated to breastfeed an orphaned baby girl belonging to my brother, who is infertile, despite my fear for my own daughter regarding the transmission of diseases or the refusal of breastfeeding?

You are not obliged to breastfeed the girl, and there is no sin in refraining. Your brother's guardianship of her does not depend on you breastfeeding her. However, if no harm comes to you and your husband consents, then it is preferable to breastfeed her so that she becomes a محرم (unmarriageable kin) to your brother.