How do I stop itching near my vaginal area? It's an allergic reaction to the detergent I used to wash clothes

Depends. If you are 100% certain it it due to detergent then some topical Hydrocortisone cream and oral Zyrtec (cetirizine) for five days will be helpful. Change detergents and do a second rinse in the washing machine. But, it's important to make sure it is not an infection (yeast, folliculitis, cellulitis).