Can you pump and have someone else feed your baby ? Is him/her still in the NICu? That would be your best bet. That way you provide him with you BM and it's benefits while you keep him from getting sick. You should try to avoid passing it to your LO as much as you can.
When LO just got home from the nicu DH had a cold also from overworking and almost no sleep, he used a mask and used clean tshirts, washed hands etc.
Keep in mind a cold is a lot more contagious at onset or first and second day.