Brief Answer:
Please read a detailed answer below
Detailed Answer:
Hi,
Thanks for writing back.
I would still keep my  differential as 
trichotillomania and weaker hair roots due to 
telogen effluvium. Both the conditions possibly induced by stress, cancer and 
chemotherapy.
Now let me summarise your skin concern as per my understanding-
"Bald patches of scalp due to hair pulling behaviour at sites where you feel hair root has become weak and hair growth is defective with frizzy lifeless hair. Also wherever the hair is pulled, you feel it grows healthy."
Now this is not due to friction from pillow, circulation problem or sweat collection.
As I mentioned earlier also trichotillomania is defined as a condition where a person pulls at hair voluntarily. The patient always complains of defective hair, sense of tension, headache etc which is relieved by hair. 
Telogen effluvium is a diffuse and acute loss of hair that you have already had post chemotherapy. Telogen effluvium takes  six to nine months to resolve. So weaker hair root can be contributed to your chemotherapy and cancer.
Having said this patchy hair fall points more towards trichotillomania.
Firstly  I would stress that you stop tugging at your hair. If you feel that the hair is defective , lifeless and sticking out abnormally, please meet a 
dermatologist to get your hair examined. The more you pull your hair, the more damaged it becomes. To treat your dull dry hair, use warm olive oil once in a week. use minoxidil solution 2 percent 1 ml two times in a day. Minoxidil will improve your hair texture, increase hair growth and strengthen hair root.
if still the hair pulling behaviours continues, you may have to take drugs like 
fluoxetine or sertraline to control behaviour. 
Other possibilities for patchy hair loss is 
fungal infection and 
alopecia areata. But these two conditions need treatment and do not improve merely by pulling the hair
For further discussion, I need the images. The same can be uploaded by clicking on upload report/ image icon, which us on right side of query page.
Warm Regards