I agree with part of what you say: Our world's wars and other horrors don't necessarily point us to God's love. If we only look at the bad things in the world, we might conclude God doesn't care about us.
But what do these wars and other tragedies point to? They point us to another reality: the reality of human sin. They tell us something is radically wrong with the world and that "something" was caused by our rebellion against God. When God created the world it was perfect, and God pronounced it "very good" (Genesis 1:31). But then our first parents rebelled against God and we've been living with the terrible consequences ever since.
But this isn't the whole picture! How do I know God loves us? I know it because Jesus Christ demonstrated God's love by coming down from heaven to defeat sin. By His death and resurrection, Christ defeated Satan and some day the final battle will be won and sin will be destroyed forever. The Bible says, "The reason the Son of God appeared was to destroy the devil's work" (1 John 3:8).
Do you want to know if God loves us and if He loves you? Look at Christ. He loves you so much that He was willing to give His life for your salvation. Yes, we live in a tragic, sin-scarred world. But Christ came to make all things new and this can begin in your life today.