My bb also three months, I use bb-car already la, my bb is ok woo... but I will take a bath for her every time after we go home la. I think if you go back to your mother's home with your husband you can try to use bb-car ka.. It will be more comfort.. ( because your husband can help!) but if you go alone, no need la, it will be better to holding her/him...la..
Nurse said not to use stroller for the first 2 months. For 2-4 months, b can only lie flat on the stroller, as spine is not strong enough to sit, so pls don't but b in sitting position in stroller until after 4 months.