The photos you posted are definitely of some sort of bedbug (family Cimicidae). They don’t produce any kind of venom, although their saliva does have compounds that prevent blood clotting and act as anesthetics so that they can feed during the night unmolested. The saliva is injected under the skin, so it’s not transmitted to other people. Most people don’t really have any reaction to the bites, since they don’t contain anything specifically meant to cause a reaction, but some people do experience an immune reaction to them (only ~30% do). That is caused by your own body’s immune system reacting to the saliva, it’s not really caused by the saliva itself. That reaction also can’t be spread from person to person. Since it’s your own body producing the reaction, that means that how you’re affected will vary. Many times people develop worse symptoms through time as they are exposed to bites (that’s probably as bad as they’ll get, it’s very rare for bedbug bites to be worse than that- but that could explain why you said that previous bed bug bites would go away quickly and this time they don’t). I will say that you probably shouldn’t be scratching them too much… it won’t really help anything, and it could potentially lead to infection.
If you want to read more about it, there are a lot of resources out there. The main one I used is this paper, although there are many less technical sources out there.