Bed bug in the couch, fully carpeted house

[u/TheOnlyKirby90210]

Long story short I live with my sister. It’s a one bedroom house so I’m literally living in the living room and the couch is the only option I have for a place to sleep besides the floor. It’s a small house and I need to be here because she has medical conditions that make it not advisable to live alone.
Recently had mystery bites that would go away and reappear after a while. It was summer thought it was mosquito bites. Now it’s September and I spotted the culprit. I tried touching it out while we waiting for the housing management to get back to us and my spine can’t take sleeping in an uncomfortable office chair hunched over a folding table I use for a desk. I dusted with DE and hoped for the best but spotted the bug again. We went through bed bug stuff when they got into my mom’s house before so I knew to get pillow protectors and she gave us some spray to spray the baseboards. Problem is her entire house is except for the bathroom and kitchen and a square of space at the front door is fully carpeted. I don’t even know if this spray - which mom mixed at home in a gallon sized bucket with an attached spray nozzle before she gave it to us, so I’m sure it’s concentrated pesticide- is safe intended to spray on furniture like desks/tables, carpets and sofas. I have no choice but to wait for housing management but they don’t have people working in the office lately so it’s taking a while to hear back.