Oh poor you! Really sympathise here. We had a nightmare with a bedbug infestation a few years back; probably picked up from a hotel and brought back on luggage. By the time we realised what was happening we had a nasty infection and had to treat a 4 bed Victorian terrace house housing us and 3 kids! Bed bugs spread quickly!
We also had cats, so initially we wondered if the bites could be fleas and sprayed for fleas, but the bites kept appearing and got worse. Bed bug bites are fairly distinctive: often on lower limbs and torso, they were itchy and sort of 'flat', round and red, and often appeared in little rows of around 3 bites. We had bed bugs.
We had a quote from pest control firms but they were expensive, and all of them were pessimistic about reinfection, so we decided to tackle this ourselves. We wanted to stop reinfection as well as stop the current infection. This is how we got rid of them, though it took a while to ensure they'd all gone and was a messy process at times.
First thing to realise is that the bugs come out at night and are attracted to you, you are their food source, so you need to stop them from reaching you in your bed.
Bought special mattress/pillow zipped covers to completely enclose all the mattresses and pillows and stop any bugs hiding in them. Even if you threw away your current mattress/pillows and bought new ones, they would get reinfected quickly, so it's important to cover and enclose them to protect them from future infection. Wrapping in sealed plastic sheets is another cheaper alternative though unpleasant to sleep on. Before the covers went on we vacuumed all the mattresses/pillows first, then steamed all the seams (which is where the bugs hide), then when everything dried we enclosed them in the new covers. Bed bugs can survive for at least 12 months without food so the covers stayed on for 2 years! - only then did we replace the mattresses.
Then we worked room by room starting with the worst room where the infection had started, and was at its worst. Cleared as much as we could out of the room, we fully wrapped soft things like cushions or soft toys in sealed plastic (or threw them out), and completely wrapped upholstered chairs in sealed plastic. All the sealed soft items we kept went into the freezer for 2 weeks (had to clear this out first!) as bed bugs can't survive freezing.
Then cleared and vacuumed each room, and steamed/sprayed(with bed bug killer spray, safe for kids, bought online) all the skirting boards, around beds etc.Had to be very thorough as bed bugs can get in through impossibly small gaps. Next, put a couple of rows of double sided tape around all the doorframe and floor to that room as a physical barrier because bugs cannot physically cross sticky boundaries.
Finally the worst bit, but ultimately the most effective, was to sprinkle a very fine white powder (bought a huge tub online and used all of it) over all the bedroom carpets, using extra next to skirting boards and around the base of the bed frames. Again, the bugs can't physically cross this barrier. This was a really messy process and meant we were all covered in bits of powder while it was down - had to use a sticky roller on uniforms before the kids went out to school every day - and had to vacuum/resprinkle the powder most days, but after 2 weeks this had worked well. For the first few days we could see bed bugs which had been trapped in the powder (yuk!), but they'd stopped almost appearing after a couple of weeks. Mind you, I kept the powder sprinked along the skirtings and around the base of the beds for months, just to make sure they'd been defeated.
tbh it was a nightmare for a month or so, and added a lot of work but was successful in the end. You need to be determined and thorough to beat the blighters but it can be done. Good luck!!