It's still very likely the spider walked on his merry way and something else happened to your hand before/after that. Especially if you don't see fang marks (though not all spider bites will have visible fang marks, of course- it's just one indicator). Though my sympathies if it is a spider bite of the not-deadly-but-still-poison variety.
I once saw a wolf spider rear up and sink his (adorable little) fangs into my shin. I didn't even know they could/did bite humans until then. Didn't hurt, but for a week or so afterward you could distinctly see the two puncture wounds, like from a tiny vampire. That's the only impact it had on my life at all.
That said, if you live in an area where fatally venomous spiders tend to thrive, I'd say go to the doctor anyway simply because it's better to be safe than sorry. But the number of people who don't live in those areas and who go to the doctor flipping out thinking a black widow crawled out of a crate of grapes or something to hunt them down is a problem- statistically you're probably more likely to die of some rare disease you picked up off the grapes.
You'll fit right in.
