Your experience is real to you. That's what matters. Your truth may not be the same as other peoples' truth, but that doesn't make it false. Don't let others make you feel like your experience is illigitimate. They haven't been through what you have.
I'm really sorry about your family. It's one thing to deny your diagnosis, but to also accuse you of attention seeking is disgusting. Unfortunately, the general public has a really inaccurate concept of bipolar disorder (and mental illness itself). I was diagnosed in 2008 and I think my parents are finally getting it. They never denied my diagnosis, they just had no concept of mental illness. They couldn't understand why I couldn't "snap myself out of" depression.
Don't worry about trying to convince people of your diagnosis. It's exhausting and not really their business. It's between you and your doctor. Surround yourself with people who support you. During a six week manic episode, I had an affair with my ex, told my husband I was leaving him, was verbally and psychologically abusive to him (eg bragging about the sex, etc), and I relapsed on alcohol. And you know what he said as he was moving out? "Call me whenever you need me. I'll be there to catch you when you fall." That was five years ago and we are doing great. He knew me for who I really am and understood that I was not myself at the time. He was still extremely hurt and it took a long time for him to get over it. I was in disbelief at what I had done, but I didn't try to make excuses, because that would be like saying his experience was illigitimate. I have to accept the consequences of my actions, even if I didn't do them intentionally or in my right mind.
I kind of went on a tangent there, but what I was trying to say is that you will find people who will be supportive. Just stay true to yourself and focus on getting healthy.