Honestly what helps may actually differ some depending on if your manic states are Bipolar episodes or if they're BPD mood swings. Bipolar mania has a stronger biochemical basis (which is why it responds to medication) and isn't something you can really calm yourself down from as much as just learn to manage until the episode ends.
I find my hypomania tends to manifest like you describe, extreme anger at the slightest things. Being active helps, I don't even mean going to the gym just finding some way to move and burn off energy. I like to just walk around my neighborhood for hours when possible. If you can buy a punching bag or create something similar (full bag of laundry hung from the ceiling maybe?) that could help diffuse some of the anger. At the times you need to rest taking long showers is good, progressive relaxation helps me some with racing thoughts so I can sleep a couple hours. Sleeping and making sure you eat and stay hydrated is extremely important to prevent mania from becoming worse, force yourself to do those things even if they seem unnecessary.
With BPD mood swings there's more you can do in regards to calming yourself down, it's still not perfect and distress tolerance is part of it but BPD swings are more reactive than they are chemical and are much shorter as a result. When I get angry due to my BPD I find writing down everything I'm pissed about helps, even better if I can vent it all in a text to a friend. If possible forcing yourself to do something that usually makes you feel good can help, the idea is inducing a mood swing to the other end of things. I'm of course not advocating self medicating but if you have a healthy hobby that makes you feel nice that's a good option. It can be hard to make yourself do those things in the middle of a mood swing but if you can manage it often does help some because BPD moods are very changeable.
If you've never looked into DBT skills I would recommend it, particularly the skill called opposite action but also any of the distress tolerance skills. You say your moods seem to fit better with BPD and DBT is one of the primary forms of therapy for that disorder. Opposite action helps me a lot when my anger develops destructive urges. And you gotta hear me out because it really does sound like the dumbest shit but me and my partner (who also has BPD) both find it helpful. Basically whatever your mood is making you want to do, you go do the opposite of. An example would be if I'm pissed and want to yell at my partner about everything he's ever done to irritate me I would instead write a list of things I love about him and show it to him. It kinda forces your brain into a different mindset which doesn't do much with Bipolar swings but can be the key to dealing with BPD.
