You could use Melaleuca oil also known as Tea Tree Oil or Melaleuca Tea Tree Oil. Very useful multi-purpose all natural medicine for cuts, scrapes, bites, stings, Etc.(though i would check on the reliability of the company you get the product from cause some are not as high quality or effective as other brands). After cleaning the bites in anyway that you prefer, apply the oil with a q-tip or (after washing your hands) directly with your finger onto the bites. This will also help along with the other advice you get. I do suggest that since they are getting bigger perhaps even apply a covering such as a band aid or gauze or something over the bits (optional put some kind of topical thing on thing on the bite in addition to the oil before covering.) (You may also look for other tea tree oil products in gel form or other).
Wash the ant bite using soap and water, and then rinse it several times with hydrogen peroxide during the day before using any other remedies. Cleaning the ant bite will eliminate most of the sting and prevent any infection. You can also apply an antibiotic ointment to the bite so as to keep out the bacteria which can cause an infection.