God is not punishing you. That's not how He works. In fact, He is extra close to you right now because when people are suffering, He draws especially close and is filled with compassion and a desire to be there for you. I so understand the way you describe you are feeling and I have felt many of those same things. What helped was to read the psalms as many of the authors felt the same way. As well, to recall that many of God's people have suffered a lot - take Joseph or Job for example.
You are not being punished. In fact, the Lord knows how hard it was to try to care for your mother. He is not keeping track of how many times you were impatient. If anything, He just wants to hold you close to His heart and tell you what a good job you did caring for her, because even though it was so hard for you, you kept trying. He is not a fairweather friend. He is constant and unchanging. Ask Him to forgive you for anything you are carrying guilt over, believe He has and allow yourself to forgive yourself. He is love and He doesn't want you to live under guilt.
I just want to encourage you that although life doesn't play fair, God does. Something from my own journey, comes to mind. I once was upset with Him and said I just couldn't get over all that He was allowing in my life that was so hard to deal with. I then had a thought come in my mind at that very moment that surprised me and has stayed with me. It was basically "No, you have it wrong. If you only knew how much worse it would be if God was NOT protecting you. It's only this hard because He IS helping." That sort of woke me up.
In North America, we have been pretty cushioned from a lot of stuff and have come to expect life to go along smoothly but now we are getting a more realistic glimpse of what people go through in most parts of the world - it's hard to make a go at things. That's why the bible is full of exhortations to endure patiently, to pray without ceasing, to hope, to not lose heart etc. because God wants us to aquire the strength and skill to survive, thrive and navigate through this crazy world. :0) And the awesome thing is, when depression and pain press in too strong for us to even practice those skills, like the footprints poem says, He carries us. I have no doubt He is carrying you right now.
Do you pray? Just tell Him the same thing you told us all here. It might feel good to get it all out that way. You don't have to hold anything back. Let Him listen. And know He hears.
I have felt much as you describe, and it isn't easy. Just remember, it's not personal, kay? God is for you and not against you.