Is there a way to check my Pokémon's EV point totals in Pokémon White?
If you're after exact values, then no - the only way to get those is if you have kept track of everything that Pokémon has battled against (and gained experience from), or if you are able to dump the save game and load it into a tool like Pokésav.
According to Bulbapedia, there's an NPC in Opelucid City which can tell you if the first Pokémon in your party has reached the 510 EV limit, but that doesn't tell you anything about which stats they're distributed in.
If you know the IVs of your Pokémon, you can plot all of the relevant values into the stat formula, and then you'll be able to solve for the unknown EV - but since you need 4 EVs for 1 stat point at level 100, you can't determine an exact value, only a range of possible values (the size of the range depends on your level).
You can also get a bunch of EV-reducing Berries (26 are required to bring a stat from 255 EVs to 0), and then use them reset all EVs to 0. You can then either EV train your Pokémon as you desire, or, if you have a sufficiently high level to calculate accurate IVs, you can do that, reload without saving, and then calculate an EV range as I described before.
There is an online tool called PokeCheck which can tell you any Pokemon's exact stats. It works by using a proxy an "intercepting" your connection to the GTS (note, it will not actually put the Pokemon on the GTS, it always returns an error message).
Just follow instructions on the site and it will show you the exact EVs and IVs of your Pokemon.