My family & I have experienced with bed bugs & cat fleas issue before.
For the bed bugs issue, it happened during one of the warmer months when we tend to sweat a lot. A few of us noticed that my dad has lot of skin "bruises" with blood stain on his arms, legs and that he keeps scratching his body due to itchiness. We too felt that our body were itchy at times. Then we saw some bugs crawling on our living room sofa and realized that it was bed bugs. We managed to trace it to my dad's bed which was infested with bugs & its eggs (literally armies of bed bugs crawling at the edges of the mattress & under it, all over the wooden bed support), blood stains all over the beds & smelly too. Apparently, due to old age & other health issues, my dad was not even awared that he has been bitten by bed bugs repeatedly for a few months. When he felt itchy, he will scratch, sometimes crushing the bugs & leaving smelly blood stains, but mostly his scratching action caused his "fragile" skin to tear & bleed.
What we did was that we threw away his bed & mattress, spray the corners of his room with some chemicals, vacuum his room as well as the sofa, washing the clothes with warm water ... did the trick to rid our house from bed bugs.
What I believe is that the bed bugs need to eat human blood to survive & will stay close to its food source. The warm weather & the smelly sweat will activate & attract the bed bugs. Some bed bugs might actually be from the wooden furniture (its eggs activated by our sweat). IMHO, throwing away everything that you suspect might have bed bugs is just unnecessary & wasteful.
The cat flea issues (originated from my workplace) was actually more frightening that the bed bugs ... 'cos the flea can jump around. Hence, spraying chemicals at the room corners is not useful. Chemical fogging is suggested by the internet. But what we did was basically washing clothes with hot water, wearing socks & jeans that cover our legs, daily vacuum of our house. Of course, I observe the basic common sense of going directly into the bathroom, shower & change of clothes immediately after I step foot into the house & before I enter my room. Again, we do not panic by throwing away clothes or things.