If two psychiatirsts have diagnosed you with BP2 then you probably have it, you're just in denial. My dad actually wrote a letter to my pdoc saying I was faking it for attention because I lived in my sister's shadow, I hope they're more accepting than that. Half my family and friends are the same, I internalise a lot of symptoms - it's really difficult and how I've not been arrested for assualt or destruction of property is a sheer miracle - or they come out in strange ways that unless people live with me they don't notice- like feverishly doing coursework, or SI, intense anger, a love of all this housework, extreme delusions etc.
I know it's hard because you want your family to be supportive, but right now think of you, keep a mood diary so you can look back over it and see what your mindset was really like, even if you do it throughout the day with the rapid cycling. You can see where you mood goes up, and down, then over time get a picture and maybe get a bit closer to accepting the diagnosis. It's also just a good way to take stock and work out where you are, if you've had a particularly emotional, or busy day.
Sorry I've never taken lamitcal, if you aren't sure then properly speak to your pdoc about it. Good luck with everything, and the dissertation.