I pick my elbows/head/feet- the skin until it bleed. I also bite inside of my cheek.It relaxes me and is a bit of an obsession. I don't want to hurt myself. Is it still self-harm?

Yes! it is considered self-harm as you are subconsciously hurting yourself, you are aware of what you are doing but still continuing with it so in a way it's intentional and it will count as self-harm along with the fact that it sounds like a coping mechanism for you, so both things indicate it to be self-harm.

You might not desire to hurt yourself, yes. But it still would be considered self harm because it is a coping skill in some form and causes physical injury.

Generally, it should be considered self-harm as you are harming yourself, regardless of the fact that it is by accident and you aren't meaning to harm yourself.

yes you are deliberately taking part in an action which is directly causing negative outcomes for you and your body, even if you do not consciously try to cause yourself harm, it has both become a method of coping for you as you said it relaxes you, and this particular method is un healthy due to the damage it can cause to your skin and inner cheeks, also you said it has become an obsessions, and obsessions in themselves can be dangerous despite weather the action itself is dangerous or not just by the pure nature of obseessions because it can be something you wish to do at all times and may take over time in you schedule better use by a different activity or distort your focus from more important things. and also with an activity that is unhealthy to begin with becoming an obsession is especially damaging because it can quickly become the only visible way to deal with the stres sof life and make it more difficult to learn positive coping methods. it is both self harm and mental self harm.

Yes, this is self-harm. When you pick your skin, it can also be known as dermatillomania or excoriation disorder. Any thing that causes pain to the body on purpose whether that's for punishment or for the calming feelings or such, is classed as self harm. there are other ways to inflict pain onto the body which can counteract the urges such as rubbing an ice cube on the place you would harm or gripping an icecube tightly, writing on yourself with a red marker, snapping a rubber band on your wrist, there are many things to stop the urges.