What an insightful young woman you are. I’m glad that you are reaching out for help with your confusing and painful emotions and trying to figure out what to do to feel better. I agree with you and with your doctor. What you are describing does sounds like characteristics of Borderline Personality Disorder. The fact that you are in your first relationship, and with someone you have a connection to is likely heightening your fears and insecurities, but is probably not causing them.
Please reach out to a psychotherapist in your area who specializes in working with BPD to get an official diagnosis, and to get help to understand and manage your intense emotions, change what you believe about yourself, and to learn more effective ways of relating to others. The good news is that treatment is available and can be very effective, but it will take a long-term commitment to healing on your part. Dialectical Behavior Therapy is among the most effective treatments for BPD. I urge you to contact your doctor to get a referral to a therapist or to click the Find Help link at the top of this page and find a therapist who specializes in personality disorders and begin your journey of healing.
Take good care of yourself.