Well, you already know that your monthly budget is incredibly tight. On the plus side, you'll feel any changes you make immediately. Good for you on getting started!
$150/month on electricity seems very high to me, although this could be a regional thing. What's the square footage of your place, and how many kWh do you use in a month? Ditto gas. Do you use it for cooking, heat, or both?
Is the $6/month life insurance policy ON your child? If so, why do you feel like you need this? Are there family health problems that might make your son difficult to insure in the future? What's the reasoning behind the critical care insurance?
Does your wife also breastfeed and/or pump? If not, it could help you save on formula.
I would break out the grocery/household budget line into separate lines for groceries, household items, baby supplies, and personal care items. They're all very different kinds of expenses, and you'll want to know how much you're spending on each. Ditto on your misc. Since you included baby items in both lines, that suggests that you don't really know where your money is going. Use Mint, or a notebook, or Excel, or whatever you like, but track every penny you spend for a month. It's really illuminating!
What is your second college degree in? And how are you absolutely confident that it will lead to a better job and not just new loans?