I'm sorry you are suffering so acutely today, Sunflower. I feel you on the bouts of wanting to get away, not go home, overwhelmed (thankfully not to a high degree recently, in my case). That overwhelm was part of what ratcheted up my drinking - and in a given night it might "take the edge off" the feelings for a brief period but would inflame the hell out of them as I drank more. I'm learning just how much as I continue managing stuff without that "helper."
I don't know if any of these would be useful to you but my too-pissed/overwhelmed-to-want-to-go-home standbys include going to a movie I know will normally be immersive to me; spending time with someone who loves and supports me, like driving yo see my parents or catching friend for a grousing visit; wearing myself out with yard work - not housework, that just makes me more irritated; or reading something on mindfulness (practicing mindfulness, before i developed those muscles while more calm, generally did not work when really activated, other than simple grounding techniques, but downloading and reading one of the books geared towards suffering/struggle would usually grab me enough to de-escalate).
Working out can go either way, usually the endorphin/chemical changes just increase aggression-unless I just keep plugging at it until exhausted. So to be helpful I have to work out extra-long and hard or do something like walking in an area of our open space land that doesn't see much traffic-for a good while.
It also sounds like you may need to talk with your prescriber? My wife takes a lot of meds and we've seen a long list of side effects. Some are temporary, some indicate a bad fit, some indicate a dosage change may be needed. My empathy to you for having to go through the med on-boarding while navigating the early steps of recovery - tough cookie!
There are a few things I've learned reading your posts over the past three weeks, Sun, you are smart, strong, insightful, compassionate, willing to reach out for help, and motivated to get through the overwhelm. I can't relate to being a SAHM or parent while managing the course on quitting drinking. I have had the ability to isolate when needed, and ride out the early phases of quitting smoking and drinking. Hats off to you and others going clean for and around your children.