I have personally walked out this question with my son. Over 15 years ago he was so sick that he had to be rushed to a children’s hospital. The physicians were certain that he had cancer based on the levels of his blood counts. After blood transfusions and multiple tests that went on for years, they finally ruled out cancer. During those years of waiting and believing God for a miracle healing, I studied the Word and read many books on healing. The entire time I desperately sought the Holy Spirit for answers and direction. 

The Lord began to teach me His ways concerning authority, healing and faith. I then transitioned from pretended faith (when my actions were fear based instead of faith based) and I connected with the Lord in a greater way in true relationship. I focused my attention on knowing God instead of seeking a healing for my son, and that was when I just knew the healing was going to happen. Though it took years, faith replaced my doubts and fear.
I encourage you to deal openly with your fears. Ask the Lord to increase your faith. Faith is trusting in the Lord that develops as you come to really know and understand Him. Faith produces the release of the healing power that was purchased by the Lord by the stripes He took on his back. 

Though at times it is so difficult to continue to believe for the promise of healing, you must spend your effort on learning about the Lord. Renewing your mind by reading the Word of God is a necessary discipline that you need to continue as you seek wisdom from the Lord concerning your prayers. To keep from growing weary, I spent many hours listening to worship music and building up my spirit man. Speak to the Lord and tell Him your fears and concerns then ask Him to take away your unbelief. To overcome the sickness, you must grow in faith for the healing.

To finally see the manifestation of my son’s healing (as well as many other trials I have walked through) was a process that required intimate relationship with the Lord. He will lead you into all truth if you open your spiritual ears to hear what the Spirit is saying. I had to break generational curses. Circumstances arose that supernaturally revealed that I had taken on a curse from my Native American heritage. I had to repent of identifying with my natural heritage and embrace my heritage in Christ Jesus. This is just one example of the layer after layer of revelation and change of thinking that I endured as I walked out the promise of healing. Only the Holy Spirit can lead us on this path of victory. Every situation has a unique way of escape that God has ordained. We will count it joy if we learn of our Lord thereby overcoming the attack of the enemy. 

Many times people settle for the doctrines of man and do not yield to the Holy Spirit as the teacher. If you are fighting an attack in any area of your life, then understand that, more than likely, the enemy is using your lack of knowledge to wear you down. If you do not understand that spiritual law is at work in your situation and that you need the Holy Spirit to direct your path to overcome the enemy, then you won’t receive the next step towards freedom. Our strength to overcome and not grow weary lies in our relationship with the Lord. Spend time in worship. Spend time studying the gospels to know Jesus and how He reacted to sickness. Spend time asking the Holy Spirit to teach you about this Jesus who died for you to overcome the enemy. Spend time getting to know Jesus and learn to trust Him. As your relationship with Jesus becomes the focus of your life, the faith to overcome will flood your heart. The healing is in the presence of the Lord. Your strength is in the presence of the Lord. Spend time in His presence. Go to meetings and conferences where Jesus is lifted up and worship is intense. I pray that this will help you refocus and find refreshing in the presence of the Lord so that you will not grow weary as you continue to grow in faith.