Is It Proper to Ask God to Heal You in Jesus’ Name?

No.

Such a prayer does not agree with what God reveals in 1 Peter 2:24 – that you were healed by Jesus’ stripes.  To ask God to heal you in Jesus’ name is to ask God in Jesus’ name to do something that He already did as far as He is concerned.  Proper responses would be to command sickness to leave your body (Mark 11:23) or to believe that you receive when you pray the healing that God already made available to you (Mark 11:24).  In that sense, you can “ask” the Father in Jesus’ name, but your prayer must be an act of faith where you definitely receive something.  You must not see your prayer as a “request” that you will wait and see if God will fulfill.