Are you allowed to have feelings of anger toward Hashem or must you work on your emunah to stop those feelings? Why did Hashem create the world if He was planning on filling it with pain and suffering?

One should not get angry towards anyone, and how much more so towards G-d, Who is the ultimate of truth and goodness. G-d's creation is not only good, but perfect, and the pain and suffering are results of man's free-will which is essentially good and pleasureful, but must include the possibility of choosing wrong. We have no clear idea when and why a person suffers or faces challenges. Life is full of challenges, and it is up to us to use all of them to grow, to destine our fate. The connection between tshuva (improvement) and suffering is only one of millions of possibilities, but definitely not definite, nor essential. Nothing is automatic nor simplistic. Just remember the parable, like a loving Father does everything towards his child out of love, but the child clearly doesn't always understand why it's in his benefit. Similarly, we accept everything Hashem sends us, believing it's all out of love and for the best, yet often it takes years to realize what good came out of something which seemed at first terrible. Also, we must remember our humility, for just as there are many topics in the world which I don't understand, e.g. quantum physics, these challenges are in that category as well. Remembering these givens will essentially resolve any kind of anger one may have.