Liking Doctor Who does not make you a nerd. Liking Doctor Who used to make you a nerd, when the Doctor was Peter Cushing or Paul McGann, and the budget was enough for paint and a trash can. You even sort of get a nerd pass if you started liking Doctor Who as soon as Christopher Eccleston reappeared. But the Doctor now wears ladies' trousers and an ironic bowtie, and the animation's not done in MS Paint.
Liking sci-fi that everyone else likes is, by definition, not nerdy. To be a nerd, you have to be still upset about Starbuck, or prefer Sienar Fleet Systems to Kuat Drive Yards, or know one of Tom Bombadil's songs, or have an opinion on Riker's beard, and you probably have--let's face it--about 6 Charisma. People judge you because you once got into an embarrassing argument somewhere public about Arwen and Glorfindel, and maybe you own some little elf miniatures, which you have lovingly painted.
Glasses and ill-fitting clothes and the new Star Trek don't count. That movie made a gazillion dollars and you bought those trousers at Urban Outfitters. This is nerd chic, a nostalgie d'Atari, if you will. It's trendy, but it's fake, and it will pass.
If there's no stigma, it doesn't make you a nerd.