What’s the quickest way to get rid of larvaes and [clothing] moths at home

We've moved to this apartment two months ago. The apartment was apparently repainted, while the building is no older than 10 years, but every single part of seems intact for all these years. I've been trying to clean eveywhere, but not fully done, yet.

Since day 1 I've been noticing small "fluff"s on walls and ceilings, the back side of wooden drawers (where they have this thin raw-wood-looking layer), and corners of the carpet in the bedroom [that is the only room with a fitted carpet and have been very curious about them, until I've just recently learnt that they're larvae, the baby(?) of the random flying moth we happen to see here and there, and that it's too late when one actually happens to see the flying moths, since it's the larvae that eats stuff, before turning into a moth.

Growing with Persian carpets, we've always had special powder killers to protect the expensive hand-woven carpets, that are informally called "carpet powder/poison", and never even had so many moths in real life! However I don't have access to that specific powder at the moment, and I don't know what actual chemicals it's got in it.

What I've done so far is:

1. regularly vacuuming the house, trying to get rid of those fluffs as much as possible (before knowing how damaging they can be).

2. spraying the two cans of "ant killer" and "fly & mosquito killer"s after cleaning every single corner (just after moving), and on a [somewhat] regular basis, but mainly to get rid of spiders that seem to an undetachable part of daily life here, and I haven't found them so strong.

3. hanging wardrobe dehumidifiers in each wardrobe that consist of a pack of silicon balls that absorb humidity and melt in the container, each of which last for a month.

4. running the electric dehumidifier that can suck something like 2, 3 liters of water in every several hours of running (not running it too frequently since it's slightly noisy and not welcomed during hours after work!)

5. reading a lot of articles online about this creature and ways of fighting against them. Additionally I've checked several products on Amazon, etc. and obviously all of them claim they have the best solution to this issue.

What I would like to learn:

is the quickest (and possibly the cheapest) way of getting a rescue from these little annoying creatures despite the articles that mention once the larvae is there, it's too difficult to immune the whole area and kill them all.

Note: We have a small "room" that contains the hot press, and the rest of unwanted/unused crap that has a room with gaps around, and I haven't scrubbed it so far, but I've sprayed the killers in there a few times, as well, but I'm still paranoid that it's the lovely home for all the unwanted insects and spiders and crawlies we may have.

The floorings are wooden (mainly) with some nylon carpets that aren't fancy enough for the larvae to eat, tiles in the bathroom, and carpet in one of the bedrooms that was shampooed and vacuumed and lots of its fluff came off during shampooing, which is another clue! and we're located having a nice view of the river/sea from our windows (which means a lot to these creatures!)

TL;DR: I need a recommendation on the quickest solution to kill all the larvae and moths that have lived in a house for quite a while without being cleaned. (Some product that can kill spiders is a pro!)

Any brands or specific product names are welcome (if that doesn't break S.E.'s rules).