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

Definitely!

Matthew 15:30-31 shows that Jesus healed the maimed.  He is the same yesterday, today and forever (Hebrews 13:8), so the maimed can still be healed today in His name.  In Luke 22:50-51, Jesus restored an ear that Peter cut off with a sword.  That was certainly unrelated to any sickness.  Sickness itself can maim people, but people can be maimed without sickness being involved.  Healing belongs to those people as well.

Jesus took not only your sicknesses, but also your pains (Isaiah 53:4).  God is the Lord your Physician (Exodus 15:26), regardless of the cause of your bodily trouble.  Any physician will treat both sicknesses and injuries!  Peter declares that you were physically healed in 1 Peter 2:24.  That is a blanket statement that healing is yours, regardless of the cause of the need for it.

A woman we know had collapsed arches due to a mishap; after we laid hands on her in the name of Jesus, she was able to run for the first time in 20 years or so.  Another woman had to have a disc in her back surgically removed because it was crushed in an accident.  After we laid hands on her in the name of Jesus, Jesus put a new disc in her back and she later got the X-rays to prove it, much to the shock of her chiropractor!  A friend of ours saw a titanium rod disappear that the surgeons had implanted in someone.  Jesus has definitely made healing available for the maimed today!