Yes, it's normal. It's something I believe all of us go with. A lot of depression is a consequence of early sobriety, and it goes away in time.
But a lot of it, especially the guilt, can stick around. It wont go away; it needs to be dealt with. I can't tell you exactly how to go about it, but good suggestions are here already.
And writing a suicide note is a lot like finding a lump. It's often nothing serious, but you don't want to ignore it. If you think you may be having suicidal thoughts than you need to speak to someone in a medical/psychiatric field. There are often charitable and government programs run by specialists in many areas if you're uninsured. And if you are certain you are having suicidal thoughts, 911 or a hotline (don't be afraid to call them; I used to work for one, we're very nice and trained.)
But as I was saying before. Depression and guilt are things that can be lessened and fixed with some work and patience. And there are a lot of resources in psychology, self-help books, things like that, which can guide you through.
And DayTrader made a good suggestion of talking to a doctor about the possibility of medication.
Take care, you. Don't feel like you need to suffer through this. Help is out there and it wants to help.