(Small note: not a mental health professional or anything along those lines, just giving advice based on what would have helped me
).
Hi OP, sorry this is probably a slightly late response but I was looking through Mental Health and I didn't want to read and run.
First off, I'm really sorry both you and your daughter are going through this. I hope you have some additional support that you can access while you try to support her! If she's got a counsellor and GP appointment, that's great as a first step and she's on the road to recovery. Has she expressed any reasoning for why she feels she needs to / has been self harming?
From the perspective of someone who suffered disordered eating and cutting from a little younger than your daughter's age, the best thing you can do is be empathetic, and avoid getting stuck in your own shame spiral (e.g. address any of your negative emotions with a support system that doesn't involve her, like a partner or therapist, and try to keep in mind that your guilt may end up unintentionally causing her guilt). I know that can be challenging and may be hard to hear, but if you can keep it together for right now then that will help by not put any more pressure or worry on her shoulders about how you're coping.
If she's got a GP's appointment, I think the next natural step on her progression is probably a CAHMS mental health assessment. That can either go well or poorly (full disclosure: I had a shit experience with them at around 11/12 for self harm and suicide but I know it's really helped some people). If she's not already diagnosed, there's a potential for that to lead to a depression diagnosis due to her self harming, which depending on her preferences, could lead to anti-depressants. I started taking Sertraline as my first anti-depressant and I think that's the one they tend to start most people on, especially adolescents.
I'm not sure if you have any prior experience of cutting (?) but I think it's important to know that like all addictive behaviours, it's not a linear pathway to recovery. There will be highs and lows and try to avoid taking it as either a flaw on your part or on the part of your daughter. If it brings you any comfort, I did it around her age to avoid committing suicide so it can sometimes be a preventative (and therefore hopeful) measure. Also, a point to be noted is that for me, there needed to be a replacement behaviour. I was self harming to cope, and so people telling me I needed to stop doing that didn't help if they couldn't provide another method to help me cope - there needed to be the yang (self care) to my yin (self harm), as cheesy as that sounds. If she has any special interests, or things that make her happy even if it's going out for ice-cream, then what could be useful is promising to participate in something related to it anytime she feels the urge to cut or purge.
Re; telling her about your own disordered eating, I would say it could be a good idea providing you treaded lightly. E.g. not saying "this is how my eating disorder manifested, this is what I did" as that could be triggering, but I think you could say "I had a similar thing when I was young, so I'm always here to support you and you're not alone."
However try to avoid mentioning methods of purging or really anything related to weight, as these are common triggers for relapse.
Social media can be toxic in relation to self harming behaviours, especially sites like Tumblr (lots of glorification of mental health issues) but keep in mind that there is a reason why susceptible young people are drawn to those sites. Even if she's seen a photo of self harm or something similar and thought "That looks cool, I'll try that" it will usually still be to escape some pain. Happy people aren't taken in by this stuff. So I'd be a bit wary about pinning too much to social media.
This also ties into not doing anything drastic. I see you've mentioned wanting to wrap her up in a blanket (which is lovely) and I think you absolutely should give her all the affection you can. However, anything dramatic like making her delete her social media / take the door off the hinges / lock up the kitchen cabinets all add to the feeling of being out of control. I'm not saying you'd do this, but I think when someone you love is hurting themselves you want to do what's practically safest even if it's not great for their state of mind. So, try and remain level-headed and empathetic is my over-arching advice.
There was also an NHS article here; (^www.nhs.uk/news/mental-health/nearly-quarter-14-year-old-girls-uk-self-harming-charity-reports/^) that states that nearly a quarter of 14 year old girls self harm, so this is a problem but you are not alone in this and neither is she.
I'm going to leave you with some links for additional support here.
This (^youngminds.org.uk/find-help/for-parents/parents-guide-to-support-a-z/parents-guide-to-support-self-harm/^) is the Young Minds' Parents Guide for supporting young people with self harming problems. It's got some recovery videos that you may find comforting. There's also a Parent's Helpline: 0808 802 5544 providing you are in the UK.
If your daughter needs confidential support, up until age 19 she can ring or chat with Childline: 0800 1111. There's an online login at the Childline website if she prefers messaging.
This (https://www.mind.org.uk/information-support/types-of-mental-health-problems/self-harm/helping-yourself-now/^) is the Mind website, which has a list of potential tips / distractions from the compulsion to self harm. Maybe good to have a look through and see if any would work for DD. I would also highly recommend this as a list of distractions from the Adolescent Self Injury Foundation. (https://www.adolescentselfinjuryfoundation.com/things-to-do-besides-self-harm^)
And for you, in case it gets too much text SHOUT to 85258 for some free text-based support and advice. Here's a link to the site: (^giveusashout.org/^)
Sorry that turned out to be such a massive post, but I really hope it helps and I wish you and DD all the best with the recovery process. Tons of luck and blessings your way, best wishes 