If a person's mother is having back pain and she request him to apply medicine and massage a little. Is it ok for the son to do it?
It would be better if it is done by her husband or a female. However if they are not available it is also permitted for a mahram male to do it.
عن جابر، أن أم سلمة، استأذنت رسول الله صلى الله عليه وسلم في الحجامة فأمر النبي صلى الله عليه وسلم أبا طيبة أن يحجمها قال: حسبت أنه قال: كان أخاها من الرضاعة، أو غلاما لم يحتلم
It was narrated from Jabir that Umm Salamah asked the Messenger of Allah (ﷺ) for permission for cupping, and the Prophet (ﷺ) told Abu Taibah to treat her with cupping.
He said: “I think he said: ‘He was her brother through breastfeeding, or a young boy who had not reached puberty.”’
Also note that some do not consider the back to be 'awrah with respect to mahrams. e.g. the Shafi'is only consider the 'awrah of a mahram female to be the area between the navel to the knees based on the hadith.