This very much depends on the severity of the condition and what skin type you have and your age.
Keloid scars can take longer if your skin is dark brown or black, due to the amount of melanin, and is usually faster if you are pale or even very fair. If the outbreak was for just a few weeks, you are under 30 and have fair skin, you can probably expect it to be very much improved within a month, if you have dark skin, the scars may take longer and leave a slight bump in the skin. If you had cysts too, again, that might take up to six months to really settle - but you can speed up healing by eating the right diet and putting the right things on you skin.
Whatever skin you have, make sure you keep the area clean and well hydrated, so twice a day, cleanse and moisturise (with a low-oil moisturiser). Aloe vera daily can also help, or products containing it (always check on the ingredients list that it is pure Aloe Vera and not a tiny bit mixed with glycerin, which is common. Also Vitamin A etc and a number of other predicted targeted at this problem.
Although the sun can damage skin, when it burns, there is good evidence to suggest that some sun exposure helps acne to heal. Just don’t burn your skin and use a SPF appropriate for the strength of the sun and you skin type.
Hope it heals fast.