On Hereditary Influence
Our OP asked a very simple question after explaining that they will soon reveal their symptoms of depression to their family, but fear they will not accept or understand it. The turmoil of mental illness seems absent in their immediate family, so they wished to gain some insight ahead of the conversation. 'Can Mentlal Illness be passed down in a family, but skip a generation?'
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Mental illness is a wide spectrum, and depression: its own branching spectrum. There could be residuals of this in all your family members, some more than others.
It was strange the ways I had to find out about mental illness in my family. As I grew up phrases like "we don't get along" were code for severe alcoholic(an uncle), like "don't worry about him" and "it's not your fault" were code for mentally unfit to raise a child and there's nothing we can do about it(my dad), like "you're nothing like your brother" were code for I want to believe you are well but just different and I'm too afraid if that's wrong.
My brother is extremely successful, married, and had a second child last year, got through college, had literally one job his whole youth before he built something of a following to sustain his dream-job and family. He seems perfectly content, and I have to say he got (nearly;) all the dominant genes. But trying to get him to understand why I couldn't achieve what he did is impossible. Simply because he was raised the same way I was - ignorant to the idea that the physical brain could be flawed.
Since my family on all sides is too stubborn to seek medical attention, we're all pretty much pretending to be well. My Aunt is a bit sloth-like(perhaps autistic) but an absolute sweetheart and very openminded. Dad is a pill-poppin roid-head rage-addict but i never starved or got kidnapped so he has that going for him. Mom is a Saint, rather too supportive, but emotionally blank. Paternal Uncle is normal, Paternal Grandmother was normal -(cant say about either Grandpas they died while I was quite young)- Maternal Grandmother also considered a severe alcoholic along with a slew of mental health issues.
So there are certainly signs of it here and there but not throughout the whole family; just taking my own experience into account. Had all my family gotten mental health check-ups, it might be a different story. I might be with a clear diagnosis and not pursued illicit substances as a treatment for what I didn't know I had.
I applaud your courage to bring to light your ailment, and I fear- (again, from my own experience)- that it might prompt them to take action. Be weary.
It's important that they understand not to overwhelm you with their solutions or their thoughts about how you feel or how you should feel. And ignore those too who are afraid to admit there own flaws- the ones who try to discredit the reality of mental illness.
Trekking through my life oblivious to the inevitable progression of the illness, then losing the ability to prevent manic and depressive states, then came the family 'cures' and having to combat it by educating myself--- So naturally I was on my own. It's still not easy to get them on the same page, but perhaps you will have better luck.
I wish things could have gone better, and I know there's no hard feelings between us. Point is I see now that had I accepted sooner that I had a chronic and progressing illness, I might have been able to help my family understand. There are a few that still accept me though.
While I trust there will be acceptance for you- given my experience was before the internet could correct people- I find there is still limited awareness about having a person with depression in your life; what that's like, and how to interact. Overall I encourage you to continue pursuing a greater understanding of your individual needs, and also seeking aid here from those who've experienced mental illness.
Secondly I recommend seeking 2 medical opinions. Perhaps a third if both recommend medicating. Medication is not always the answer, money wont buy what you will learn on your own with understanding your needs and aligning you're daily-self-maintenance with your fluctuating emotions. Medication comes after that alignment. Otherwise it's throwing mentos in a coke bottle.