You can use diy bedbug treatment around cats and you need to do it asap.
I am in the US and can buy spray that comes in a battery powered sprayer bottle. This is the best option if you can lay your hands on it as the spray is evenly applied and the nozzle can be used at odd angles. Saves your hand from fatigue too.
You can also buy powder.
To tackle the bugs, every single drawer of every single chest and wardrobe in your room must be carefully emptied. All removed items must be carefully placed in black bin bags, sealed, washed and preferably dried in a dryer.
Non clothing items must be wet washed using bedbug spray. The furniture must all be pulled away from walls and sprayed inside and out, paying particular attention to corners.with the furniture away from the wall you spray the wainscoting and floor near the walls. Built in wardrobes must also be emptied and sprayed. Don't forget doors.
You need to take all bedding off the bed too, place it in bin bags, seal them, and it must all be hot washed and preferably dryer dried.
For clothing and bedding, try a commercial diy laundromat if you don't have a dryer.
Handle all clothing and bedding very carefully.
Whatever clothing you have on needs to be taken off and put in the bags too. If you have clothing that is just out of the dryer or off the line wear this while you work, then it too must be washed and you can put on items you just cleaned.
All footwear must be sprayed inside and out.
The bed itself must be sprayed, as well as the head board. The mattress needs to be inspected thoroughly and sprayed all over, particularly the seams.
The whole floor needs to be sprayed - you will have to move the furniture around to do this. The doorway, doorposts, and lintel need to be sprayed too.
If you want to be extra thorough you can do the whole house.
If you bring the clothing and bedding to a laundromat in your car wearing the clothes you wore while working in your room/ house, you will need to spray the car too. This is an incredibly hard thing to do but it's not worth taking chances.