I am about to graduate from college with a minor in psychology, and am diagnosed with BPD as well... I'll try to use myself as an example of a typical person with BPD.
From my understanding, the core characteristic of BPD is difficulty regulating emotions. I tend to feel everything very intensely. Anger, happiness, depression, anxiety, embarrassment, guilt, etc. are usually at about an 8 on a scale from 1 to 10 for me. Things that the average person might be able to shrug off, I often can't. (Though, therapy has been helping with that.) I get mood swings that are often triggered by small events, and sometimes they just happen. Like you said, there is a back and forth between happiness and depression several times a day.
Because I'm so sensitive, it's fairly easy to make me angry or to hurt me if I'm close to someone and care about their opinion. On top of that, sometimes I can be impulsive and very quick to jump to conclusions or make negative assumptions, which means that if I don't have my BPD under control, sometimes dealing with me can be like walking on eggshells.
There is a tendency for me to see life in a very black and white way. At a given moment, my feelings about relationships, friends, family, school, or life in general are either very good, or very bad, rather than the in between "not perfect, but still okay." Because of this, I tend to do something called "splitting" when it comes to close relationships with an individual: at one moment I might love someone and completely idealize them, and at another moment I may hate them and think that they are the worst person alive. I sometimes go from one to the other very quickly. People with BPD are infamous for having passionate but unstable relationships.
People with BPD tend to be VERY sensitive to criticism, and have a very disordered way of thinking, which this article on the site explains more about:
http://www.bpdrecovery.com/TwistedThinking Personally, I suspect that the root of BPD is an underlying and persistent feeling of worthlessness and helplessness. The vast majority of people with BPD suffered from sexual, physical, or/and emotional abuse in childhood. It is hard for a lot of us to feel close to other people, or loved, even though I am sometimes desperately lonely.
The constant mood swings and instability are often accompanied by depression, anxiety, difficulty concentrating, reckless behavior (drinking, smoking, shopping sprees, promiscuous sex, etc.), self destructiveness. Honestly, I have problems with all of these categories, though some people with BPD only have troubles with a few.
I think if you compare your symptoms to my description, it looks like BPD is probably the right diagnosis for you.