Coughs and colds are extremely common in young children and tend to occur more frequently over the autumn and winter months. They are usually caused by an infection and most children get better by themselves. In general, antibiotics do not make them better more quickly. If they are finding it hard to breath or are too breathless to feed, they may need to be looked after in hospital.
It is unlikely that this is linked to Covid-19, but as we are in a pandemic, see this information here.