Do this shortly before you move, like a week or two. You can apply it immediately, but reapply it before you move.
Buy a really good vacuum cleaner, one with a Hepa filter or one specifically for pet hair/fur, if you don't already have one. DE (see below) is highly abrasive and the particles are very, very fine.
Buy a 10lb to 20lb sack of food grade diatomaceous earth (DE from here on) off Amazon. This one comes with an applicator. Use the applicator to apply it around all the baseboards, kitchen cabinets and drawers, dresser drawers, etc, etc, etc. Next take a dishtowel or similar cloth, lay it flat on the counter and put a handful of DE in it. Wrap it up so you have kind of a cloth bag full of DE. Now take this around to all the carpeted areas and pat the bag as you walk around. You want the DE to "poof" out into the air and form a cloud, then settle on the carpet.
You can get the DE into your electronics, but you'll want to take them apart and blow them out with compressed air after you move.
DE is not harmful to humans, you can stick a finger into it and suck the DE off the finger. It is safe for children and pets but lethal to most insects.
Get this and dust the ever living shit out of everything. Puff it into all the nooks and crannies you see termite holes in.
We had a bad flea infestation not too long ago and if they get into your carpet there’s some powder that my vet friend recommended because it’s safe for cats to be around after the dust settles, HARRIS Diatomaceous Earth Food Grade, 10lb with Powder Duster Included in The Bag https://www.amazon.com/dp/B01N39V5SU/ref=cm_sw_r_cp_api_glt_fabc_5Z4C681Q7GA4AEZ5HXJJ?_encoding=UTF8&psc=1
Just make sure it’s the food grade kind. It is very powdery so I would recommend a mask to use it
Okay so this isn’t the best answer bc it causes dust BUT. I’m one of those people who seems to be especially delicious to fleas and I feel your pain. They’re horrible to get rid of but a groomer actually gave me some advice that I’ve used in three houses to cure fleas.
Go get a bag (or five depending on how much space you have) of Diatomaceous Earth. Dust a generous amount around the outside of your house - any potential entry points especially. Then very finely dust all your carpet with it and use a broom to work it into the fibers. I also put it in window frames (in the actual window tracks), door frames, etc.
The way this stuff works is that it’s full of harmless (to you) sharp edges that cut the limbs off small insects (even big ones like spiders) and then the salt content dehydrates their bodies from the inside.
It’s safe to breath (I still use a mask while dusting it into the carpets just bc), it’s safe for the cat and you guys to walk around on and be exposed to, and the food grade won’t poison you (just don’t go dusting your pots and pans yeah?).
It does cause a fine dust as you walk around the house. I vacuumed every few days to get the dust and all the dead critters, and then worked a fresh layer into the house.
Every single time I’ve used this in conjunction with laundry and flea treatments for the pets, it’s worked like magic. Months of fighting fleas and this had the bites stopped in a week every time.
Pro tip. This also worked for a cockroach infestation and a bed bug infestation in two separate houses.
Renting sucks, the potential for critters is rough but this stuff does amazing work and I highly highly suggest it.
Suffer the dust for a month, maybe six weeks and then consistently keep doing it on the entrances and outside.
Get food-grade though.
This is what I've used in the past to keep my neighbors bugs from becoming my bugs:
Thank me later: HARRIS Diatomaceous Earth Food Grade, 10lb with Powder Duster Included in The Bag https://www.amazon.com/dp/B01N39V5SU/ref=cm_sw_r_cp_api_glt_fabc_SEJS1X3NCSYE2FDP56MS?_encoding=UTF8&psc=1
Im starting my first grow also heard ladybugs are bad to be around plants not sure tho Was told this is good to keep pest away https://www.amazon.com/dp/B01N39V5SU?ref=ppx_pop_mob_ap_share