Do NOT sell your car. When your SO mentions they may not love you all the time you don't want to sell your only means of transportation. And after hearing that I would move myself back home if at all possible
Go to every target, walmart, starbucks,shoe store etc within twenty minutes of your home and apply. Try to talk to someone there. They may tell you to use the app thing there or apply at home but you may get to talk to someone.
Drop the internet and phones. Make a list of priorities. Not paying rent will get you evicted. Not paying a internet bill just means no internet and eventually maybe collections but you still have a roof over your head. Do you have car payments? Don't want a car repossessed.
The dogs can eat crap food for a little bit. They may have an upset stomach, but they will live.
Google food pantries in your area and see what it takes to go to them. Getting food through them will help you have money for gas.
Did I see you were pregnant? You should be able to get ins and some assistance like foodstamps while you are(you could here anyway).
Try thinking long term. Do you need to look into rehoming a dog? Selling your car for a cheaper beater? Maybe something better on gas? get down to no cable or cell phones for a while and just have rent and utilities.