A very serious question on family, depression and forgiveness?

Me and my partner have been together for 2 years and have an amazing 10 months old child together. When we 1st got together we were so well suited. I thought i had found my soul mate, but since every thing is falling apart around us. For the past year we have struggled with no money, and our family's have not helped us out with our child like we thought they would. We don't get any time together and all we do is bicker and argue. Sometimes we have mega arguments and my partner will end up self harming and cutting herself, She has a terrible temper and will lash out at me at times. She is 22 and i am 27. Friday night everything fell to bits. She went out, got drunk and the slimy barman offered to walk her home, And they kissed. She admitted that to me the next day and now she has moved out of town and back with her parents with our child and i am alone and down. She said she feels so low, that i never say anything nice about her, am not loving, and always having a go at her. I know she loves me and i love her. We both love our child. We have had such a tough 2 years and had no luck at all. I miss them so much but how can i forgive her for cheating. It makes me feel sick. I think she may be depressed, and maybe it is my fault but i never deserved this. What now? Do i just walk away and be a part time dad? I feel hurt and embarred. I would of married this girl if we could stop the arguing but now i do not see a way back