How can I let my parents know I'm not depressed?

Agree to one visit to the doctor.
The doctor can tell, after that consult, that indeed you are not depressed.
They can put that as a statement on paper, which you can hand out to your parents.
For now, for whatever reason, it seems they just can’t/won’t take your word for it, but from a professional they likely will.

It does seem odd that you spend a lot of time in a dark room playing with your phone. Do you have air conditioning in your house? Are you saying that you need to keep the windows open and then use the curtains as a bug shield?

I can understand your reluctance to have friends over if your parents are always arguing.

Don’t you ever want to just hang out with someone? Why do you need to plan in advance?

I take you at your word, but I can understand your parents’ concern. I go along with @rebbel‘s suggestion of seeing a doctor or therapist. At the very least they may explain to your parents why you don’t want to have anyone over if they are always arguing.

First of all, don’t over play it. Be natural, be yourself. Don’t let what they think get you down or they’ll feel that about you for sure.

As a natural born smart aleck, I would totally be chipper and happy around them, then back to normal in my room.

BUT, it wouldn’t kill you to see a therapist. Most everyone does anymore, it’s nice to have someone to talk to.

And who knows, if you tell the therapist the arguing is what’s upsetting you and why you don’t want friends over, maybe your PARENTS will get some therapy or a divorce, or do something to fix that situation.

And by the way, I’m sorry they argue in front of you or they’re unhappy. Just remember that’s not your fault or responsibility to fix, it’s theirs. You sound like a normal teen to me.

It’s possible that you ARE depressed. The onset of depression isn’t always obvious to the one with it. This article:
https://www.webmd.com/depression/guide/teen-depression#1
gives a good overview of teen depression. You do have some of the causes and symptoms. Your parents arguing could be a contributor. Your original question didn’t give indications of how your school life is, but that might contribute. You sound like you have a withdrawl from your friends. These are all things that could play into it.
On the other hand, you might want to take a Meyers-Briggs test to help see what your personality type is. You might just be more introverted than they like. That doesn’t mean you are depressed or there is anything wrong with you…you just “recharge” your batteries best when you are by yourself.
I’m with some of the others here…go to the therapist. Let a professional take do some tests to see what they say. If you aren’t depressed, there won’t be any blowback. If you are, (s)he might be able to offer some suggestions to eliminate or deal with the things that are causing the depression.

By telling them and showing them by smiling and other things. You can’t fake depression because your body language speaks volumes but I am glad you aren’t depressed. Good for you.

How others interpret your mental state can be determined by their opinion of you. I used to live with someone who was certain I was mentally ill. Therefore everything I did was interpreted in that light. They were even actively trying to get me committed to a mental hospital!

I finally realized my smartest move would be to agree to go to a mental health expert to be evaluated (one that I chose for myself) as long as they also agreed to be evaluated!

The verdict? I was not crazy, but they were of questionable mental health!