What's usually recommended for getting rid of mosquito bites fast?

Not possible: Although topical cortisone may work but would not work overnight. Injecting the area with kenalog (triamcinolone) may, but it would be like swatting a fly with a hammer.

May decrease sx's: Store aloe vera gel in refrigerator & apply to affected area. Rub basil leaf on bite. It repels mosquitoes & has anti-inflammatory effect. Consider applying calamine lotion or crushed ice or a cold pack. A 1 to 1 mix of water & baking soda is effective when applied to lesions. You can take oral medications like Benadryl (diphenhydramine) or Chlorpheniramine for itching.