Is it possible for a mum to get stressed and over fatigued while breastfeeding and taking care of the baby?

Yes, you will definitely feel worn out if you do not have extra family member to help you in taking care of baby. I suggest you can talk to your husband and let him understand how you feel and to see if he can have some share in baby taking e.g. in charge with the baby after he returns from work. If this is not workable, you can try to ask family member e.g. MIL or your own mother/father to help you. If there is no help from family member, you can consider to hire a maid too.