From personal experience my DS2 caught a nasty cold when he was a few days old too. It was a bit of a nightmare at the time but he soon got over it and constant breastmilk seemed to really comfort him. He has rarely been sick since then though

My boytwin was also sick at less than 2 weeks old, although much more severely. I continued breastfeeding him throughout his time in hospital and the doctors were astonished how fast he recovered (from almost needing ventilated, to going home within I think it was 7 days). I chose to be grateful that breastmilk helped him recover faster, rather than let him down in his getting ill in the first place.