Nursing sick twins

Shanae • Strong mother strong sons 👶🏽👶🏽
My twin boys are only one month old, for the past week my boys have been sneezing a lot and had a little mucus I told their doctor she told me not to worry just pay attention to the sneezing. This week it got worst, their mucus has build up more and they're having difficulty breathing at times.  I remember my aunt told me I have two choices suck it out from the nose or blow through the mouth I find blowing through the mouth helps more. I use saline to help out also. They're getting  a little better I do this every two to three hours when they seem fussy. 
I'm still breastfeed which is very difficult; for starters I'm not producing enough so they stay on for 30-40 mins feeding ( break in between) and they don't sleep as much, they only sleep on me or next to me, Now I feel myself getting sick, is it still safe to breastfeed? 
Side note : there's a draft in the house that got them sick