If you assume the Bible and stories in the New Testament are true and a historical account, then yes Jesus healed people.
This is what I believe. I also believe that Jesus still heals people today. He is still doing miracles. What is curious to me is how Christians want to make a system out of it. Like almost use Jesus to help people get better.
Not all Christians are this way, but some are. Healing is used to gain money, position, popularity and/or power. I think it is possible for someone to use God's name to heal people and not know Jesus.
What made me think of all this is the question that came to me yesterday: Did Jesus heal everyone? Yes, he healed everyone who asked him to.
Not many accounts are in the Bible of people getting healed. There are no mass healings (not that he doesn't or can't do this today-they just aren't recorded in the Bible.) It is fascinating if you look at what happened right before a healing occured-or in my opinion stirred Jesus do perform the miracle.
The following are different key points that moved Jesus into action:
1) Someone begging Jesus. (John 4:46)
2) Asking Jesus. (Mark 1:30, Mark 1:40, Matthew 8:5, Matthew 9:18)
3) Jesus own compassion and mercy (Luke 7:11, Matthew 20:30, Luke 22:50)
4) Others bringing the person to Jesus (Matthew 9:1, Matthew 9:32, Mark 7:31, Mark 8:22,)
5) Jesus is unaware and heals by someone touching Him. (Luke 8:43)
6) People asking Him to have mercy on them (Matthew 9:27, Matthew 15:22, Luke 17:11)
7) He purposely healed on the Sabbath to tick off the Pharisees (John 5:1, Matthew 12:10, Luke 13:10, Luke 14:1)
8) To see the wonder of God (John 9:1, John 11:1)
In conclusion there is no system to this. It seems Jesus is being Himself and the details surrounding each healing is very different and the effects are far reaching.
I do believe that Jesus did heal and still does.
I also believe He not only can heal our body, but also our spirit, heart and mind.