My 16m was down with viral infection previously but has since recovered. However she still has running nose for almost a week Other than this, she is ok overall, eating and playing well. Should I continue to monitor or bring her to the PD?

You can continue to monitor her. Importantly that her fever is no longer there.It would mean that she is on the road to recovering. If her running nose is still persisting for a month, do bring to the doctor for some flu medication which will speed up her healing process.