For a start, don't beat yourself up. Working FT with a 2yo is a lot more than many mothers do. It's hard, exhausting and puts you in a situation of survival mode that makes being proactive very difficult if not impossible. It might very well be that right now is just not the best time to consider taking on the huge demands of losing weight on top of it. The more pressure you put on yourself, the more tired you'll be, the more disheartened and depressed you'll feel, and the more you'll want to eat to make you feel better. It's a vicious circle.
So start by being kind to yourself and congratulate yourself for what you are managing to do. Then reduce your expectations for the time being and focus on the little things you can do to help yourself. Could you rely on your colleagues to give you moral support? Being able to be honest, talk about it, realise that you're not the only one, and mutually support yourself so that you at least don't eat much during the day is a good way to go about it. If breakfast is an issue, eating unhealthily, could you consider waiting until you get to work and having something there healthier?
Then try to come up with small strategies. What's your weakness that makes you binge? Take aways, cakes and biscuits, anything? If take aways, throw away all the leaflets, get rid of the apps. You won't be able to go out with your 2yo, so you need to fight the ordering.
If cake and biscuits, don't buy any, but one thing that could help is buying sugar free lollies, that you can suck to get that sugar craving. Lollies take longer to get through than a biscuit and have much fewer calories. Freeze healthy yogurt, or even if you are desperate for a bar of chocolate, buy only one, and put it in the freezer in the morning.
Tell yourself that if you are good to your standard for 5 or 6 days, having one bad day is really not so bad, no need to be filled with guilt afterwards.
As for your back, sadly, it is highly likely that what will help is exercise, gently, even through the pain. Do go and see your GP for advice though.
Think of ways you can distract yourself when the urge to eat takes over. Are there any activities or things you can do that would bring you some pleasure besides eating.
And finally, break any habits associated with eating. If you are used to eating whilst watching TV, once your child is in bed, it is going to be very hard to stop it and that's usually where most of the damage is made. So instead of focusing on not eating, focus on what else you can associate watching TV with, or what else you can do that you won't associate with eating.
Through it all, remember that you can lose weight at any time, so if right now is not the right time, next year or the year after might be so. Don't let this make you feel even more miserable.