Right. Notice Jesus didn't say, "Your good deeds have made you well..." He said, "Your faith has made you well." Jesus understands the distinction in a good deed by which one attempts to earn his healing and faith in a God who graciously gives it to whosoever asks.
Agreed. However, man left to himself doesn't realize there is God w/o Him first revealing Himself to that individual. God grants man the gift of faith, whereby he can believe.
ALSO, notice that Jesus didn't walk up to random sick people and heal them wether or not they asked for it (i.e. unconditional election). But instead he heard their cry and responded. "Humble yourself and you will be exalted."
Mark 3
1 And he entered again into the synagogue; and there was a man there which had a withered hand.
2 And they watched him, whether he would heal him on the sabbath day; that they might accuse him.
3 And he saith unto the man which had the withered hand, Stand forth.
4 And he saith unto them, Is it lawful to do good on the sabbath days, or to do evil? to save life, or to kill? But they held their peace.
5 And when he had looked round about on them with anger, being grieved for the hardness of their hearts, he saith unto the man, Stretch forth thine hand. And he stretched it out: and his hand was restored whole as the other.
I can not see here where this man went looking for Jesus to heal his withered hand. Sure, he was in the synagogue, but I can not find support that he went looking for Jesus. I think here is where Jesus was using this sick man to show the Jews that He was/is the God of the Sabbath. The same account is told in Matthew 12, and again, I can not find support this man went looking for Jesus. He was showing the Jews that by Him being Lord of the Sabbath, it is not against Jewish Law to heal on that day as well.