Well I have no babies, but I have five dogs - four small ones and a big, bounding epileptic golden retriever. I can't begin to imagine having to deal with them all needing what they need - food, cuddles, brushing, holding during a seizure - as well as dealing with a screechy and unhappy toddler. I've cared for horses too and believe me when I say I am admiring the crap out of you right now - they're such beautiful, rewarding animals but oh my god they're hard work!
Will your dogs perhaps settle down after a bit of a run around or some food? Do they respond to you flopping out and ignoring them by clambering all over you or do they get the message to chill?
When my nieces and nephews were grouchy with teething I used to bundle them up and take them for a walk. They were distracted by the sights and sounds and seemed to get a bit worn out by it as well. Maybe even a (well insulated) wander around the garden with a dog or two in tow? Might relax you as well!
I do know the ails of bad backs - what sort of pain is this? What region? I ask because heat vs. cold could be important depending on whether is muscular, joint or other skeletal, or from the bump strain. Do you have heat pads/ice packs handy that you could put on? Is the DH any good with a quick back rub? Could you take thirty minutes for yourself every day or two to have a nice warm bath and a mental unwind? Or even a lie down with a cup of your favourite warm something and a lavendar pillow?
If nothing else, take some deep breathes, close your eyes, and try to focus on just one thing - the dark behind your eyelids, a sea horizon, a babbling brook, whatever does it for you - and take a minute to shut everything out. Just find some inner calm. Yes, I know that might sound really cliche, but it really can help bring you back towards the centre.
Feel better, have some hugs, and some 