[¯|_(ツ)_|¯]

I don't think that you're being overdramatic at all, and it's not fair that your parents are telling you that just because you're thirteen that you don't have "real" problems. Mental illness such as depression can strike at any age, and this is also not the "pain olympics." Just because someone else is struggling, doesn't mean your problems are any less valid than theirs. I don't think that you're doing this for attention at all. I started struggling with more than just my lifelong anxiety at around the age you are now.
I know that you don't want to go to the hospital again, but if you're this close to suicide, maybe it's the best place to be. They can help stabilize you, whether that's with group therapy or getting you on the right medication to make sure that things are more manageable. I know when I was in the hospital I was afraid of what people would say, too, but it helped me to get away from the situations that were stressing me out until I could handle them a bit better. If anyone outside your household asks, you can just say you were away for personal reasons. If anyone in your house says something I'd say that this topic is off limits until they are better able to communicate with you.
Plus, if you tell your parents they may not leave your medications out like that anymore. I bet that they don't want you to die and would be devastated if something happened to you, and so would your sisters. Perhaps you can suggest a lock box, where they only give you access to the medications that you need for the day.
It's good that you see a therapist, even though you wish you didn't tell them that you feel sad all the time. Perhaps you can write them a letter or email where you explain some of the things you explained here in this post. For example, you can state how you are worried that people will think you're doing this for attention because you are young, and that you think people will say that you don't have any real struggles. You can also point out that you're bad at telling your emotions and explain the feelings that you explained here (you did a good job!). At least that way, you will have everything out.
Do you think that your therapist could be a resource for telling your parents how serious things are? I know that when I've been in a bad place in the past, my therapist would sit down with both my mom and me and explain some of the things I'm going through and why it is important to take those things seriously. It can help to take some of the pressure off of you if you have the therapist talk to them. The therapist is a professional, so they may have training in how to talk to parents about situations like this in a way that don't raise their defensiveness or cause an argument. It may also be more "believable" to them coming from a person of authority (although they should believe you as well!).
Don't go through this alone. There are people who love you and care about you, and would hate to have anything happen to you. I know that we care here on TeenHelp.
You can do this!