It is possible that you have had some allergic reaction due to the epilatory cream. In order to avoid this situation, it is always instructed before using any such cosmetic skin products, to undergo the skin sensitivity tests. There are also other possibilities for the underarm rash including dermatitis (atopic, contact, and allergic), heat rash, excessive sweating, folliculitis or psoriasis.
You should wash the area with hypoallergic antibacterial soap followed by rinsing thoroughly, apply moisturizer, wear loose fitting clothes and avoid deodorant / cosmetics for a couple of days. Sometimes over-the-counter hydrocortisone cream provides some relief. If still the bumps are persistent, I suggest that you consult a dermatologist who can determine the cause and prescribe appropriate treatment for it.