Well one good thing is that she too has noticed that things are not going so well with her moods. You said she starts going on a tantrum then starts crying and apologizing to you for acting crazy.
I would sit down with her when she is in a calm mood and suggest to her that her mood swings are really getting out of control and that you think that you are her should go together to the doctor and explain to him what has been happening. Explain to her of your concerns and that you want to see her happy and well again.
Maybe she would rather start with talk therapy sessions that you could also go with her to at first to help the therapist understand both of your concerns like what she has recently gone through the last few years and how bad her mood swings are and of your concerns of being bipolar.
Just try to approach her when she is in a calm state and assure her you love her and want to help her feel better and that you are also concerned because of how it affects you as well. Truth is the best medicine applied with gentleness and sincerity.