I dont know where you are from, but here I think that if you told her that she would almost definately ask more questions rather than instantly admitting you. I think she would only admit you (here) if she thought you were in significant danger of harming yourself or someone else- for e.g. if you had actually, truly tried to commit suicide before, or if you've been taking steps towards it and have a date in mind etc. I dont think its illegal for her not to admit you, its a matter of her professional judgement on your individual case.
In the least, I would tell her the antidepressants arent working. Because theres no point in going through all the counselling and the drugs if they arent working, not only do you deserve better, its also a waste of your time and money!

you can get better