For me, the diagnosis of bipolar (I have bipolar 1) diagnosis was immediate. Well, the first time in the early 80's when I was a teen it took longer. But each time I have seen people, even when I didn't tell them I had been diagnosed previously, they diagnosed me with bipolar. Sometimes within the first hour. (I have been diagnosed repeatedly due to not seeing the same therapist continuously until this past 6/7 years. If the Dr is CONVINCED (your word) that you don't have it, I would guess they were right. But they also should have an explanation to your questions.
To answer your question, Borderline Personality Disorder has similar symptoms. I don't know of other diagnosis. I suppose people that have anxiety, paranoia, OCD or have depression, might have some similar rapidly changing emotions. I don't know. The thing about bipolar is, emotions change with no trigger. Otherwise, something has to set a person off. A reason, be it medical or otherwise.
If you cannot trust your therapist, I would suggest seeing another one. If 2 or 3 all say the same thing, then the mistrust might be coming from you. Eventually, we have to give in to the facts. For me, I denied or played down and ignored my diagnosis for decades before one too many job changes forced me to accept and learn how my illness has affected (and still affects) my life.
I have read people say this, and I think its somewhat true - worry less about the title of your diagnosis, and focus on what symptoms cause extreme behaviors and work on recognition and re-direction of extremes.
For me personally, the title of my illnesses are very important and help me to feel more in control of my progress.
Best of luck to us all.