You really can't
Some insect and spider bites
have a characteristic appearance, though generally you really can't tell what bit you unless you have the critter or the carcass in hand.
The majority of insect bites do not need treatment unless from a poisonous species, or unless you have compromised health. If excessively large or swollen or infected, give you md a call.
If you live in a lyme diseas area do see md.