Welcome here. It is obvious you are very worried for your daughter, as anyone would have to be to want them to get professional help. Please excuse me, I'm not being insensitive or belittling your concerns however I do think you might need to say a little more about the things in her behavior that are troubling you.
At present you have said she only leaves her room when pressed by friends, sleeps during the day and is up at night. In the conversations you have had with her she has only mentioned 'little things'. Plus the epilepsy and telling some lies.
Does she refuse to go to school to the extent it is harming her education, is she eating properly, have you seen any signs of self-harm or drug use? Has she been bullied, is the breakup with her father affecting her - and so on.
OK, just talking in general and assuming there is something wrong I'm sure you have tried all the reasonable means to persuade her to come out, and to see a doctor, so what is left?
First Is there anyone she respects, a friend, family member of someone from school who she might take notice of?
Secondly I'd imagine setting an example by receiving treatment yourself would be appropriate, not only will she see what is involved but you can directly benefit from this yourself, and may - apart form other things in your life -find your daughter's behavior easier to cope with.
Thirdly I would expect if you have been constantly pushing her to seek help she may well be pushing back, and neither of you will get anywhere. It may be worth considering adopting a different approach where you are simply a friend and companion, trying to do things she enjoys together - perhaps it might be you going to the movies with her.
Again a general thing, many young people with low self-esteem feel they are not allowed opinions - they are simply disregarded in the decision making process. Perhaps if that is the case here then encouraging her decision making might be appropriate. Obviously not on matters of very great import to start with, however demonstrating a trust in her judgment might be helpful.
I'm afraid all of this is conjecture, and is in any case long term. Would you like to come back and say more?
I'm sorry to sl=peak so bluntly however knowing hte nature of hte problem will make thngs a lot easier