J.,
I think what you are describing could be normal, but I would encourage you to call your family doctor to discuss this in more detail. If you are suffering from some postpartum depression or any depression for that matter, it is very important to talk to someone and start some kind of treatment (medication, counseling, or both).
That being said, I am a mother of two very young children. Up until recently, my husband travelled a lot for weeks at a time. It is very hard to be home alone with a baby all day, especially when you are new at being a mom. You've only been doing this for four months--everything is so new and it can be very overwhelming in the beginning. Your fiance is your partner, your friend, your baby's father, and your helping hand--of course you are going to be upset when his day off falls through. I would also encourage you to talk to him and describe how you are feeling. Maybe if he understands better, he can help support you in other ways even if he can't physically be there.
As far as the baby crying, I know how you feel. My daughter screamed for the first five months of her life until she was finally diagnosed with reflux. It wears your nerves thin. My only advice to you is to hand the baby to your fiance or put him in a safe place like his crib when you feel the urge to yell coming on. Step outside to calm down or scream into your pillow. Take a walk if your fiance is there to care for the baby. Go to a quiet place and write down your feelings. Try to find a way to release that frustration without yelling at the baby.
Good luck to you.