Specialization right now (at this point in your ‘career’) is bad because unless you really really only want to do one kind/area of design you will find that you will get jobs in a number of areas.(exhibit/product/interface/auto/etc)
you can’t really be choosy until you develop your experience/portfolio.
look at it this way too, in a car company there might be a large design dept but only a few (relatively) companies and locations. but in product design there is everything from big corporations to small consultancies and freelance.
As a designer you will find that we are/can be jack of all trades and yes being specific gets old. (try designing high tech telephones for more than 5 years after your first few designs, with all of the accompanying crap with marketing and engineering and a micromanaging manager you’ll be dreaming of making macrame plant holders and hitting the craft show circuit)
this is just an anaolgy (based on experience)
but the grass is alwasy greener on the other side of the fence.
if you HAVE to specialize, I would get a dual major or a minor in something ‘useful’ like business, marketing, psych (for interface design) or another discipline like graphic or web design.