She doesn't need therapy, she needs a mother who is prepared to teach her about life, rather than indulging her every time she turns the waterworks on. Sorry OP, but this is on you. You should have started doing this with her from the age when you first began to see that she had too much, probably about 3, then by now it's unlikely it would have been a major issue. Our job as parents is to prepare our children for life as adults, not to give into tears and objections, as if you carry on like this, you are going to have one hell of a time with her when she reaches her teens, and tells you what a dreadful mother you are because you refuse to let her do things that she'll tell you 'all her friends do!' She'll have screaming fits, and call you all sorts of names, and what will you do then, give in and let her do something that you know she shouldn't be doing??
I think you should sit her down and explain that there is a limited amount of space in her room, she's now got to a point where she has too much stuff, and it's time to let some of it go, or she will not be able to have ANYTHING new until she does. Then stick to it, every time she sees something she wants, or asks for something new, tell her she can have it, but in order to do so, she has to get rid of something first. Also, model the same thing for yourself, so if you want to buy a new item of clothing, tell her you're going shopping for a new skirt, top, whatever, and then ask her to come and help you decide which item of clothing you should get rid of, because you haven't got room to keep buying things unless you get rid of something. Then when her birthday is approaching, tell her that you need to go through her things together and choose some things to get rid of ready for when her birthday comes, as she's bound to be given new things, and there won't be room. You can get her to choose things and put them in a box, so that if she gets 6 new toys, she can then chose 6 things of similar size, from the box to give to a younger child, or to a poorly child in hospital, which ever you think will resonate with her most.