Try to avoid giving antibiotics since they work only against bacterial conditions and not viral conditions. Antibiotics also kill the good bacteria along with the bad bacteria which is turn brings down the immunity of the child further.
For a blocked nose, you can use steamed bathroom/ saline drops/ mucous aspirator/ breastmilk squirted in the nose. This will be helpful.
In case you're still worried, please consult a breastfeeding friendly paed that's not quick to prescribe medication.