Have you got a tumble drier?
Sadly, now you (probably) have an infestation, you need to make serious efforts to destroy it. You can lose a lot of value in clothes, blankets etc.
Buy some large, clear plastic bags big enough to hold a garment on a hanger (they are cheap by the roll) and some of those plastic storage crates with a tight-sealing lid.
Modern mothproofers contain Transfluthrin, which will kill moths, larvae and eggs. It is sold in units that are just enough to treat a drawer or small cupboard by building up vapour inside. They will not build up enough vapour in a room, and it will dissipate in ventilation or break down in sunlight. It can take a couple of weeks to build up in a container. Hanging units for wardrobes usually treat half a cubic metre each.
But if you put your clothes through a tumble drier, the heat will kill larvae and eggs, and if you then seal them in a box or bag with a sachet or ball, they will not get re-infested while you deal with the outbreak. Zero-in is a good brand. You can put one ball or sachet in a pocket of each coat or suit if it is in a bag that you can tie or tape to seal. They do not smell like old mothballs and may last 3 months.
You have to clean inside, and especially behind and under, furniture and beds, and the gap under skirting boards. Frequent hoovering is best for this, especially in a baby's room where you do not want to use chemical sprays.
You can get things scented with lavender or cedar. These do not kill moths but will make your clothes smell nice when you throw them in the bin.
Examples
www.robertdyas.co.uk/catalogsearch/result/?q=Moth
www.ebay.co.uk/sch/i.html?_from=R40&_trksid=p2505460.m570.l1313&_nkw=zero+moth&_sacat=0
www.tesco.com/groceries/en-GB/products/294937409