Spider bites are completely different to mosquito bites.
(Warning: this is going to be gruesomely TMI)
Mosquito bites will have a red pinprick at the bite site, with swelling around it. If it is large, hard, and white or bruised-looking, then you are probably having an allergic reaction and need antihistamines. IME it is best to take a-hs as soon as or even before you are bitten, as they are far more effective before the swelling and itching get really bad. If the bite site gets infected you get a small yellow blister and a tight shiney red ring immediately around it.
(This is the gruesome bit) Spider bites are quite different. They start off looking like a regular bite, itchy but without the immediate area swelling, though the whole limb may swell and ache. A blister develops, which grows and spreads. Eventually the blister bursts and the flesh inside has died and comes away in lumps, layer after layer. You get an ulcer which takes a long time to heal and is very vulnerable to infection.
Humans tend to be allergic in varying degrees to the anti-coagulant that mozzies inject with their bites. Spider venom is tissue-dissolving, and humans don't tend to be allergic to it.
BTW although most spiders are venomous, very few British spiders can actually bite humans. Their mouthparts are the wrong shape.
One got me last year. British GP did not know what it was. South African friends recognised it at once.