Is the illness that afflicted me, and my constant anxiety about my health, a punishment from Allah for sins? What should I do to repent? And should I visit a sheikh who summons jinn for healing?

You must engage in sincere repentance and adhere to God’s law, for God is Forgiving and Merciful; He accepts the repentance of those who repent, and one who repents from a sin is like one who never sinned. What you feel, that God will not accept your supplication, is from the whisperings of Satan. As for your feeling of illness, it might be an illusion. Therefore, think well of God and be assured that His decree for the believer is good. You can consult doctors. Beware of listening to anyone who advises you to go to those who treat with jinn, as this is a dangerous satanic advice that imperils your faith.