incoming unsolicited advice (ignore if you want; i understand <3):
this is definitely a tough situation and i'd probably feel the same way in your shoes, but would you feel that same guilt about leaving your patients if you were physically ill and needed treatment? or i guess from the patient POV, if your provider had to go on leave for medical treatment, would you blame them or be mad at them or have any hard feelings about it at all? what about if a colleague of yours left for treatment? things happen that are out of our control; you wouldn't be abandoning anyone by seeking help for what is considered (mental) illness. or at least that's my opinion, fwiw.
i fail to take the common "approach yourself like you would a friend/someone else" advice to heart myself, but in this case i think it's very applicable (assuming you're a reasonable person who wouldn't be pissed off with someone else for being sick lol), and the thought of someone ctb'ing or just giving up on being help-able before ever even seeking help in the first place kind of bums me out. not that my feelings matter -- you get to choose what to do with your life, of course. but it would kind of suck... idk.
i'm dumb and i can't quite infer from this post if you've never had mental health treatment or if you have but it's just been non-intensive, and i don't know where you're located, butttt you could maybe look into IOP programs to minimize the time you'd have to miss work. i know people who've done things like that where they only need to be at the clinic/office/in therapy twice a week. you'd probably have to get through a DBT workbook as homework, which i'd imagine is time-consuming and exhausting, but you at least wouldn't be inpatient. i'm a hypocrite because i should probably also try more intensive therapy before killing myself or doing ECT or IV ketamine or microdosing shrooms, but do as i say, not as i do!!! (only if you want to, that is)
this whole post probably just reads like empty noise in your brain if you're actively suicidal, but if you do happen to have the energy to think about it, it's here just in case. whatever happens, i hope you find some way to feel better than you do now. i know it sucks to feel like you're not allowed to ctb because of family or other people.