Is sickness a punishment from Allah?

No, not in the way many people fear. In Islam, illness is mainly a test and a way for Allah to forgive sins and raise a person's rank. The Prophet ﷺ said that no hardship, illness or worry reaches a Muslim without Allah wiping away some of his sins. Never tell a sick person that their illness is a punishment.

Illness is a test and a mercy

Allah tells us that life includes trials:

وَلَنَبْلُوَنَّكُم بِشَىْءٍ مِّنَ ٱلْخَوْفِ وَٱلْجُوعِ وَنَقْصٍ مِّنَ ٱلْأَمْوَٰلِ وَٱلْأَنفُسِ وَٱلثَّمَرَٰتِ ۗ وَبَشِّرِ ٱلصَّـٰبِرِينَ "We will certainly test you with a touch of fear and famine and loss of property, life, and crops. Give good news to those who patiently endure." Quran 2:155

The Prophet ﷺ said: "No fatigue, nor disease, nor sorrow, nor sadness, nor hurt, nor distress befalls a Muslim, even if it were the prick he receives from a thorn, but that Allah expiates some of his sins for that" (Sahih al-Bukhari 5641). Pain is never wasted, and patience brings reward.

The best of people were tested the most

When Sa'd asked the Prophet ﷺ which people are tested most severely, he replied: "The Prophets, then the next best and the next best. A person is tested according to his religious commitment" (Sunan Ibn Majah 4023). So hardship is not a sign that Allah is displeased with you.

Prophet Ayyub (Job) suffered a long illness and called out: "I have been touched with adversity, and You are the Most Merciful of the merciful" (Quran 21:83). Allah answered him and praised him as a patient servant.

What about the verse that mentions what our hands have earned?

The Quran also says: "Whatever affliction befalls you is because of what your own hands have committed. And He pardons much" (Quran 42:30). Scholars explain that some troubles can be linked to our actions, as a reminder to turn back to Allah, but that He pardons much more than He punishes.

Nobody can know why a particular illness came. A child is born ill, a good person falls sick and a careless person stays healthy, so we never judge others by their health. Asking forgiveness is always good, but it should come with hope, not guilt. For a related question about anxiety, see Is anxiety a punishment from Allah?

What to do when you are ill

Seek treatment. The Prophet ﷺ said that Allah has created a treatment for every disease (Sahih al-Bukhari 5678), so see a doctor and take your medicine.
Be patient, without hiding your feelings. Sadness and tears are human. Patience means not complaining against Allah.
Make dua. Ask for healing, ease and forgiveness.
Keep up what you can of prayer, dhikr and Quran, in whatever position and amount you can manage.

Long illness is hard on the heart. See How do I cope with chronic illness as a Muslim? and What dua can I say when I'm sick?

With others who are sick

Comfort and encourage them, and never suggest that their illness is a result of sin. See What is the etiquette of visiting the sick in Islam?

Key points

Illness is mainly a test, a mercy and a way for sins to be forgiven.
The Prophets were tested the most, so illness is not a sign of Allah's anger.
Nobody can know why a person is ill, so never say it is a punishment.
Seek treatment, make dua and keep your hope in Allah.

Tip: When you feel low, repeat the words of Ayyub: "I have been touched with adversity, and You are the Most Merciful of the merciful." It is a prayer straight from the Quran.