If you're in the UK, there are no 'nasty bitey spiders' here.
There are lots of spiders that can give a nip if threatened enough, typically trapped in clothing or bedding and squished/pinched/crushed. If you didn't see the spider bite, you can't determine whether it is a spider bite or something else. (Even if you're a doctor, a spider expert, whatever...) - you'd need to get the venom and have it analysed at DNA level, and that would only help with an envenomated bite which many will not be.
It is not possible to determine what bit you by the bite or the resulting wound/reaction.
Two puncture marks can mean something bit you twice in the same spot, rather than being the marks from two sharp mouth-parts - mosquitos will often do this if disturbed.
People can react differently to the same insect/arthropod/thorn/splinter etc, due to different immune system responses, due to different bacteria on their skin, different wound care etc etc.
Many bite reactions are entirely down to the bacteria on your skin rather than anything the biter did/injected/whatever.
For some reason this year, unlike any other year, all the mosquito bites I have had, have gone like this image and resulted in a small fragile blister that bursts if clothing touches it, leaving a rather sticky scabby bite wound. As there are at least four species of mosquito I've identified in my home (I breed them for fish food) it is unlikely these bites were all the same species and yet all bites reacted the same... so the common denominator is me... OH has had bites and they've not reacted this way at all.