Hello and thank you for turning to HCM for your health questions!
Short answer: You should not be concerned!
Detailed answer: Apparently you got a severe
sunburn from the
tanning bed that you used! The fact that the sides of your breast are healing slowly is because the skin is more delicate, soft and vulnerable in these areas compared to other parts of the body. But do not worry, it will go away, but it will last longer.
In order to help the skin in these parts you can apply some gentle lotions containing
aloe Vera, in order to moisturize and hydrate it.
Lastly, I strongly advice you to avoid tanning beds in any circumstance because they give you ultraviolet
radiation at high doses, and it is one of the main factors increasing the risk of
skin cancer according to the most authoritative health organizations. A single exposure, as in your case, will not harm you nor increase your risk for any skin diseases, but please do not use tanning beds anymore.
I wish you a fast recovery and good luck!