Dedicated to the Lord Jesus Christ Who loved us, gave Himself for us, and washed us from our sins in His own Blood; and to the Church, which is His body.

The multitudes were thronging Jesus. That is, crowding in on all sides, so it seems strange that He would ask, "Who touched me?" 
Many people were physically touching Jesus, but one woman touched His power by faith.  Many people in the crowd probably needed healing, but she is the only one mentioned who received. The difference was the touch of faith.
If it was simply Jesus' willingness to heal that determined whether or not the healing took place, then all of the sick in this multitude would have been healed.  It's not prayer that saves the sick, but rather the prayer of faith that saves the sick (James 5:15).
Healing is governed by law and not by a case by case decision from God based on His feelings toward us. This woman received her healing by the law of faith before Jesus knew anything about her. 
Passionate pleas to God will not get the miracle we are looking for. Although Jesus is touched by our feelings, it requires faith. It's not because Jesus doesn't know our needs or hear our cries that miracles don't happen, but rather it's because very few know how the law of faith works.
One of the main differences between a God-kind of faith and a natural, human faith, which everyone has, is that human faith believes only what it can see, taste, hear, smell, or feel. God's kind of faith believes in things that cannot be seen. We must believe that we receive our answer "when we pray" - not when we see the thing we've desired. 
Simply put, faith is our response to God's ability, made complete by our actions. Trusting Him completely and, believing, then our actions will follow.