Why should my health be dismissed due to my mediocre efforts?

This one is real personal however im seeking insight about what i should do. (sorry for the long rant)

for some reason, my worth in this house equates to how often i wash the dishes, clean the bathroom, and generally help out. my family is and should be very aware of my current depression. i have been this way for a while but wasnt diagnosed until 2-3 years ago. when i was real small, i couldnt understand that feeling of ever-lasting sadness built up in my heart. ive been feeling like shit for a very long time. and every battle, no matter how small, can still be extremely difficult for me. however, i have been trying so hard to not wallow and drown in it. i try so hard, and although its not the strongest of efforts, i believe my attempts are valid regardless. and im not asking to be praised for my shite effort and contribution, i just dont believe that should define my worth of position in this dumb fucking house.

personally, i have become excellent when trying to calmly convey my feelings, as i am a big crier (no shame in being a sprinkler), but it all goes to hell when its being misinterpreted, stretched and pulled, then spewed back at me. its so hard talking to a wall that will chew up your words and spit it right back in your face. but continuing with the topic, im a lazy bastard (NOT PROUD) that has a difficult time just leaving my bed to start the day, which are some results of my thriving depression. what these soul-sucking walls cannot compute is that i do not feel 110% when it comes to chores. in their eyes the only way to help is to either send me away (again and p.s it didnt fucking help) or just revoke my basic necessities or my electronics. theyre glossing over the fact that mentally i am like this and that i in fact do not want to live in the mud and squander. my small effort i contribute is: washing only the dishes i use instead of the pile sitting by the sink, cleaning up after myself in the bathroom/kitchen, take out the trash/recycling sometimes (without being asked), help care for my baby sibling and assisting my disabled sibling. it might just be me but i do what i fucking can. and im tired of having my depression be some hoopla topic that warrants threats of being sent away just because my caregiver, MY BIRTHER, cant "be around it" bc of the way it makes them feel. and then they turn into a sobbing mess and go on about how they should just "jump off a bridge bc whats the point of living" im sorry but MY MENTAL HEALTH ISNT YOUR RAP SHEET TO CRY OVER. all they do is invalidate me, deflect their inner-most thoughts, and wont get the help either of us need.

im one year away from graduating, i have no job/experience due to my area, i have not a cent of savings to my name (no bank account) and im afraid of ending up just as the ones before me. 

i just want stability.

tl;dr - my current position in life fucking sucks boo hoo sob story about my dumb feelings towards the blood people i hate. i want to move on from this point and be in a healthier environment. i want to be somewhere ANYWHERE stable.