Bad first month in my PhD
It's your first month. You will be in the program for 3-5 years. Everyone knows this, and you will have the opportunity to redeem yourself. Be patient. Do better in the future. Everything will work out alright.

What's more important is that you understand your weaknesses. Work on them. Become a better person and scientist by figuring out how you can address your weaknesses by either addressing them directly, or working around them.