If your arm is truly broken, you need to get it evaluated because it can heal improperly and cause irreversible damage if so. I would just use the "fell down" excuse. Granted, they may give you the side eye (be skeptical) but they can't make you say you did it to yourself.

Assuming you are old enough - you could always play it off as "a drunk night" - those scenarios don't get many questions (I work in an ER). If you have SI scars, they likely won't ask about them (assuming they are not fresh) and if they do address them, tell them you are currently in treatment for them and do not offer any extra information.

I do also, think you should tell your T. Although she may be slightly disappointed in that you hurt yourself (and she doesn't want to see you hurt) - she may also be able to see just how desperately you avoided cutting yourself and perhaps offer some better coping techniques to try next time!

Big hugs and warm thoughts!