All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, is His slave and messenger.
The Jinn can possess human beings and harm them, but we do not know whether or not it can cause the illness in question. In any case, the remedy for Jinn possession is reciting Ruqyah (healing Quranic verses and supplications), sincere reliance upon Allah, and seeking His help. Verily, the one who relies upon Allah and earnestly seeks His Help never fails.
Whoever implores Allah for recovery while fulfilling all the due conditions for having his supplications accepted and recites the Ruqyah in the lawful manner, he will be successful and guided to recovery by the will of Allah.
It should be noted, though, that one should not attribute everything to the Jinn. In principle, a Muslim should take into consideration the physical means by seeking medical treatment for his illness, in compliance with the guidance of the Prophet in this regard. He should not decisively believe that his condition is the result of Jinn possession except with clear supportive evidence. Also, know that Ruqyah is effective in all cases, whether the illness is physical or caused by Jinn possession. Therefore, one should recite the Ruqyah along with utilizing the means of treatment, such as consulting physicians and the like, while relying on Allah The Exalted and asking Him for recovery.
For more benefit on the treatment for Jinn possession, please refer to Fataawa 12589, 326485 and 288775.
Allah Knows best.