Personally, I have asked God this question many times myself. I would like to share a personal story of an experience I went through, hoping it may help you learn how to deal with trials you are currently going through. There are a couple of illnesses that I've been struggling with ever since senior year of high school. I have some liver and small intestine complications. It's an autoimmune (see link for definition of autoimmune disease) disorder in both organs. One of the illnesses is known as celiac disease.(see link for information on celiac)
The process for being diagnosed, finding the right medication and the correct dosage was quite the stressful process. During this time I went through a lot of physical and emotional pain. Dragging myself from doctor to doctor hoping for a cure. Never knowing if I could be "physically able" to eat gluten again. Not having answers to my questions killed my motivation and self confidence. Could I find the right medication? Will I be able to have a normal diet, or life? I did not know where to turn. I had hit a low point in my life. After realizing that God was the only thing holding me together, I began to study the scriptures more diligently, searching for the answer to my question. 
Why does God allow suffering? I was reading in 2 Corinthians chapter 12 and received an answer to my prayers. The apostle Paul asked Jesus three times that a "thorn in the flesh" might depart from him. Jesus answers Paul in verse 9 and says,
"My grace is sufficient for thee: for my strength is made perfect in weakness."
"Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me."
The Holy Ghost entered into my heart as I read and taught me that I may never be fully healed from my "thorn in the flesh", but if I have faith in Christ and rely on His Atonement He would give me the strength to endure my infirmities. Enduring with faith in Christ is what gave me strength to go on. So again the question, Why does God allow us to suffer?
So we can learn to rely on the Savior, which enables us to grow spiritually and physically. I realized if I exercise faith in Christ He could bless me with the ability to perform admirably with my mortal infirmities. I found a better doctor and he was able to get me on correct medication so I could live a normal life. I was able to do the sports and activities I loved once again. My prayers were answered. President Dieter F. Uchtdorf, Second counselor in the First Presidency, tells us how to access the Atonement. He says,
"Having faith in Jesus Christ and in His Atonement means relying completely on Him-trusting in His infinite power, intelligence, and love. When we have faith in Christ, we trust the Lord enough to follow His commandments even when we do not completely understand the reason for them. In seeking to become more like the savior, we need to rely, through the path of true repentance, upon the merits of Jesus Christ and the blessings of His Atonement."
I was given infirmities so that I may learn to rely on the Savior's atonement and through the atonement I can grow spiritually. How great will be your reward in the eternities if you learn this doctrine in this life? This blessing is available to all people.
During my experience exercising faith in Jesus Christ, I have come to know that the Savior's atonement is real. We all must go through pain and affliction in this life on earth so we can grow. I'm not telling you this story just to make you feel sorry for me. I'm only writing this article so that others can understand that there is always hope through the Atonement of Jesus Christ. Through the power of the Atonement we can overcome whatever trial that entangles us. I invite you to exercising faith in Christ and be obedient to God's commandments. If you do so you'll access the incredible healing powers of the atonement that Christ has made possible for you.
