Hi,
If the local reaction to the mosquito bite isn’t too serious, then one just needs to relieve the itch until the swelling subsides. Non-prescription creams containing menthol offers quick itch relief - the good old “Mopiko ointment” works great.
If the local reaction is more intense, then a topical steroid cream will help reduce the swelling faster. Hydrocortisone cream is the mildest topical steroid that is available from the pharmacy without a prescription.
Stronger steroid creams will require a prescription and will be more effective than hydrocortisone cream. These include betamethasone valerate (betnovate) and mometasone furoate (elomet). Combination creams such as fucicort and fobancort work well too.
Hope this helps!