geek in colloquial usage means a highly specialized skill in one field, most often pertaining to the maths or sciences.
nerd means extremely computer oriented, generally anti-social, and correct in most grammar and spelling.
you are neither.
The words have pretty elastic definitions.
Here are my personal ones:
Nerd: someone who knows about something, and talks as if they know everything about it but does not know how said object/concept fundamentally works. They talk about this subject whether people want to hear it or not, and often push their way into conversations. Nerds are also typically (or stereotypically) antisocial and rejected.
Geek: someone who knows about something to a very fundamental level and who
discusses (I ea, has a a debate or intelligent conversation about) this subject only among his fellow geek-like peers. Geeks are generally sociable, and have a well-formed group of extremely diverse friends, which often share a common talent or goal.