I finished antibiotics for an infection but still have a lingering cough can i still be contagious?i have a one month old baby.cough is dry tickle

Difficult to say: Difficult to answer absolutely since you don't say what the infection was or what the antibiotic was. But, with that qualification, a dry lingering cough that is more of a tickle is not so likely to be due to a lingering infection, but more likely some lingering irritation. The good news is that a 1 month old baby still has a high level of maternal antibodies in its system, so may be less succept.