There are several factors that can contribute to breaking out following treatment. If you break out immediately following your treatment, within 24 hours it could be a couple things. One is the body can have a histamine reaction to actually removing the hair alone, this is common on the face where there are millions of vellus hairs a square inch. Mens backs as well can have an histamine reaction. You can consider taking an antihistamine prior or following your appointment (it is advice to consult your doctor or pharmacist prior to) to minimize reaction if this has occurred before.
You could also cause an reaction or break out by not following after care such as excising immediately following your appointment (24-48 hour), using irritating or fragrant products, exfoliating, tanning, going in a hot tub our swimming pool, wearing tight fitting clothing, touching skin with dirty hands that may have dirt and bacterial.
Furthermore, between appointments depending on hair growth, when your hair starts to grow back (10-14 day range) it is very important you have been doing proper aftercare. Exfoliating and moisturizing are EXTREMELY IMPORTANT to preventing ingrown hairs from developing. Sugaring makes your hair softer and finer and grow back patchy and the hair is weaker, if you are not exfoliating (everywhere you sugar) the mouth of the follicle can be congested and that is when you get an ingrown hair. Sugaring decongests the follicle and exfoliates dead skin but you must maintain this following your appointment 2 to 3 times a week.