Is Cryolipolysis Allowed in Islam?
Question

Is it permissible to get cryo-lipolysis done to get rid of excess fat? My reasons are purely for health and self-esteem, I observe Hijab and Niqab in accordance with Shari`ah, so this will not be to appease anyone else.
Praise be to Allah.
What is Cryolipolysis?
Cryolipolysis is one of the modern methods to eliminate excess fat in certain areas of the body, where a specialized device called Cryoshape is used to freeze the fat under the skin in a specific area of the body. Afterward, the fat cells that have been frozen die, and then the body gradually disposes of the melted fat through the liver or kidneys.
The doctor, in the fat-dissolving sessions, first anesthetizes the area to be treated with local anesthesia, and it is possible to also use a moisturizing cream to protect the skin from the cold temperature. Then, the doctor moves the Cryoshape device over the area and during this, gradually lowers its temperature until it reaches 5 degrees Celsius. Usually, the procedure does not exceed one hour per session.
Is Cryolipolysis Allowed in Islam?
The use of this method to get rid of fat is permissible with the following conditions:

It is predominantly assumed that there is no harm.
It should be done by a husband, or a woman, as long as the patient is a woman, and the purpose of the procedure is for improvement, and not for a therapeutic need.
If the fat is in the area of the `Awrah, which is between the navel and the knees, and the doctor is not the woman`s husband, then there must be a need to do it, such that the fat is excessive and cannot be eliminated by exercise or the like, and not merely for beauty and improving the figure; because the basic principle is the prohibition of a woman looking at the `Awrah of another woman.

Abu Sa`id Al-Khudri (may Laah be pleased with him) said: The Messenger of Allah (peace and blessings be upon him) said: "A man should not look at the `Awrah of another man, nor should a woman look at the `Awrah of another woman" (Reported by Muslim, 338)
An-Nawawi (may Allah have mercy on him) said in his explanation of Muslim: 
"It is forbidden for a man to look at the `Awrah of another man, and for a woman to look at the `Awrah of another woman, and there is no disagreement on this. Likewise, it is forbidden for a man to look at the `Awrah of a woman, and for a woman to look at the `Awrah of a man by consensus.
The Messenger of Allah (peace and blessings be upon him) indicated by prohibiting a man from looking at the `Awrah of another man, that looking at the `Awrah of a woman is even more forbidden.
This prohibition applies to other than spouses and masters, as for the spouses, each one of them may look at all of the `Awrah of their partner" 
An exception to this is what necessity dictates, such as looking for treatment and healing.
Therefore, if the fat is in the area of the `Awrah, and the purpose is merely for improvement and beautification, then it is not permissible.
For more details, please refer to the following answers: 152130 , 83001 , 105464 , and 13022 .
And Allah knows best.