When a Disease Is Healed, Can I Believe to Receive Healing from the Damage That It Caused?

Absolutely!

If a childhood fever left you blind, you have the right to receive healing for blindness.  If an illness you had a long time ago left you paralyzed in any part of your body, you have the right to receive healing for that paralysis.  Probably someone among the blind people Jesus healed went blind through a disease, and probably some of the paralytics were that way because of polio or some other illness.  The cause of blindness, paralysis or any other problem does not matter.  Jesus provided healing for everything that could ever go wrong in your body.

Remember, Jesus healed the maimed, not just the sick.  This would cover accident injuries as well as problems caused by diseases.

In Matthew 15:30-31, Jesus healed the maimed people in the crowd.  He is the same yesterday, today and forever, so He is still willing and able to heal the maimed today!

See also:

Can I Get Healed from Injuries from Accidents as Well as Diseases?