Welcome to HealthcareMagic.
Thank you for providing the brief history.
As what I feel is the bruishes will be because of the chemotherapy
and radiotherapy which is common as body develops too much heat.
If your mother had RA then it would have troubled the peripheral joints beforehand.
Since she had tightness in the upper back this could be the post effect of Surgery as muscle has to try balancing the removed part. So if your mother is not diabetic then you can use cold packs for back. Make sure she don't have even cold.
For shoulder pain
, I think this will be muscular. because usually people post mastectomy
complains of shoulder pain.
Using stocking for upper limb will be good to avoid swelling which occurs due lymphatic drainage
For shoulder to regain the flexibility there needs to be undergoing some sessions of physiotherapy
which can help the shoulder to avoid pain and lose the ROM.
Please feel free to contact me if you have any questions.