Sick baby and milk supply

An

My 4.5 month old is very sick with the common cold (lots of coughing, congestion, phlegm, had a high fever -yes we saw a doctor). I am exclusively breastfeeding her as she won't take a bottle (not even my pumped milk) and I'm worried my milk supply will go down since she's not nursing as long or as actively as she normally would. Is this true? Should I be pumping? Or will it be okay? She'll nurse for a few minutes but then the let down happens and she stops sucking and just lets the milk come into her mouth. After that she'll be done. I'm worried she's going to lose some weight too.