Hi, sorry to hear that you're feeling this way. It sounds extremely similar to what I went through when my daughter was born. The most important thing to keep in mind is that it gets better. The first four months after my daughter arrived were the most unhappy I've ever been in my life, but after that things started to become easier and parental responsibilities felt more fulfilling.

I'd strongly recommend seeing a therapist. You might also want to see if you can arrange your schedule to get more sleep; I know it might seem counterproductive when you already feel a lot of time pressure, but sleep deprivation is absolute torture and makes everything worse. Getting my daughter on a regular sleep schedule was the single biggest life-satisfaction improvement I've ever experienced.