Covid vaccine while breastfeeding a sick baby?

My husband wants us to get the vaccine after hearing of his sister having covid and not doing very well. My 15 month old is currently sick. Either a cold or allergies (leaning towards allergies due to itchy watery eyes and constant sneezing) I currently breastfeed him. He just got his 15 month vaccines 4 days ago. Would It be safe to get the vaccine while he’s still sick and it being close to his vaccines since he’s taking my breast milk or should I wait for him to get better before I get it?