You have red and elevated patches of nickel size( You mean a coin I hope) Mosquito bite are usually small but some one is allergic to them can get them bigger also,or it may a Urticaria
to insect bite ,we need to know these patches are only on exposed part of body or all over body . Because bite occurs only in exposed part while other allergy
may involve other part also.We may need to rule out any viral infection or blood abnormality?
There is no itching it may subside by itself . soothing lotion may be applied if itching is there a anti allergy medicine OTC may be used . If is alarming and increasing see a Doctor for help and proper treatment.
Best of Luck