I was 'diagnosed' with BPD (comorbid with GAD, depression and PTSD) and after a pretty intensive course of DBT I no longer meet the diagnostic criteria for BPD and I feel like I've really turned it around. However, I was incredibly fortunate to have a GP who's known me for my entire life who was able to give me the proper referrals, and a wonderful support network of social workers and psychiatrists. My therapy was done privately as DBT isn't offered on the NHS in my area, and as far as I know (at the time I started) it isn't available anywhere else without going private - there are plenty of medical professionals who haven't even heard of it!
As others have mentioned, your age is going to be a major barrier to getting a diagnosis for a personality disorder, and your GP won't be able to give you the diagnosis anyway; you'd need to see a psychiatrist, and even then, they're often quite hesitant to give a diagnosis on something like that. I was never formally diagnosed (hence the 'diagnosed' up there) so it doesn't appear on my medical records, but my psychiatrist was able to identify the thought patterns associated with it, and sent the referral for DBT on the basis that it would help with the way my depression manifested - we both agreed that CBT wouldn't be appropriate for my needs.
The main thing is to find out if your parents can afford private treatment for you (I think mine was about £80/hour with one or two sessions a week over the space of five or six months, so it's really not a cheap option) or if your primary care trust is willing to fund it, if it's not available on the NHS in your area. Often a therapist will do a free or fixed-rate introductory session where they assess your needs and determine whether the therapy is appropriate for your situation. Your psychiatrist may have a list of recommended/approved therapists so you can phone around and see what's available close to you.