Technically, yes, that is a form of self harm. Really, any intentional harm to your body is classified as self harm. Now, disclaimer, I am not a therapist in any way, but I have dealt with self harm and associated things in my life as well as currently. 

One thing that I suggest for anxiety that has really helped me with my own anxiety disorder is to see your anxiety as a separate person or being aside from yourself. Almost like an AE. A lot of times, we tend to think that we are our emotions, when in truth, we are not only our emotions. I see my anxiety as my little panicky friend in the form of a little puff ball. [i'm strange, ok?] and it helps to disassociate myself from the panic. It also can help you focus on something other than the true panic. 

Now, it doesn't work 100% of the time and not a lot for the really bad panic attacks, but for me, it helps.

Also, I would suggest talking to your parents. I understand your hesitation, but if you are having this anxiety and these panic attacks, you need to tell someone so that they can get you the help you need. 

And lastly, a way I've found that is helpful sometimes to stop myself from harming myself, is to take a hair band or a rubber band and lightly snap it on your wrist. It will provide the feeling that scratching gives you, but without the harm to your body.

I hope my ramblings helped, and I'll pray for you.

Stay Alive, Fren |-/ [twenty øne piløts reference, by the way.] 

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Your scratching does count as self-harm, yes. I looked up "dreamy drunk feeling anxiety" and found something by someone called Kiri, who explained that it's called depersonalization or derealization, and that good things to do are to go out and look at things and touch things, to be present in the world, figure out what causes it and avoid those things. You're not going crazy. Commenters suggested trying new things, expressing suppressed emotions, finding stability, and smiling. Yes, smiling, even if you're unhappy; it can make you feel better, strangely enough. Another search result said to treat it like something fun, like a lucid dream; to try enjoying it. 

"Derealization anxiety" turned up lots of informational and help sites, so you can try that. I'm not sure what you're looking for. The Internet will probably have it, though.

I don't think it's quite the same, but I sometimes get a feeling like nothing is real. It's not scary; it's kind of like how I imagine being in zero gravity, if that was combined with the sensations of being dizzy, watching a movie and dreaming. I can hear myself talk, but I'm almost not the one speaking. It's harder to keep track of things outside my vision, and it doesn't feel like what I see is actually there. It's weird, but it's fun. I can't control when it comes, although that usually seems to be when I'm tired, so I treat it like an opportunity and experiment with it, laughing at whatever happens. It came recently when I was in the woods, moving fallen branches off a trail. I was concerned about hitting my head on something, so I imagined that I was watching a video, and some reality returned. 

Hope this helps! 

Self harm is anything done to intentionally cause pain to yourself.  So yes it is self harm, but in the way the term is used generally nowadays, yours is not as much self harm as it is a coping mechanism.  As Admin said, it sounds like it's become habit more than anything.  So as they suggested, try rubbing instead of scratching.  Other less harmful tricks are holding a piece of ice or using a rubber band or pony tail holder.  Sometimes the most helpful thing can just be to have something to do with your hands.  Fidgit spinners, despite their obscene popularity, are actually pretty good with coping with anxiety and nervous energy. Having something to ground yourself can make a real difference.

I'm very personally familiar with self harm, and I strongly suggest finding another way to cope before you start to get desperate for something more.  With a need to feel comes a great amount of desire and desperation.  If it intensifies, or continues, I'd strongly suggest talking to your parents.  Any form of anxiety that starts to become more than you know how to handle needs to be quickly addressed before it becomes overwhelming.  If it starts to become overwhelming, especially the older you get, the more tempted you'll be to find something stronger to deal with it.  Don't let it get to that point.  You'd be surprised how much having someone else who knows can help.  Even if your parents aren't sure how to help with it, they'll help you find ways to not only manage but overcome it.  And if nothing else, having support means the world.

I truly hope and pray you are able to find a better way and are able to overcome your anxiety!  It's important to take care of yourself and put yourself first sometimes.  Don't be afraid to ask for help.