Try using a bigger pad because if your period can't hold your flow and it is going all over your pants then your pad is probably too small.
get on pill may help if your not on it happened to me for many years or go see obgyn they can help
You could also try using a menstrual cup or tampon alone with a long pad just in case you're seriously nervous. They don't take your virginity and you can't feel them (when properly inserted).
Like another comment said, birth control can help with long or heavy periods. It has been prescribed by many doctors for those specific reasons.
My period has done this many times, so I wear a tampon and a pad on my really heavy day.
I'd say your flow becomes heavier when you sit down, it happens 2 me too, especially on my heavier flow days. It's nothing 2 worry about, I would suggest just changing your pad more often, I like 2 change mine every 2 hours, I was wondering if you could answer my question??