Do I still have a claim if the accident is partly my fault?

Not in Virginia, no.

A lot of places in the US use "comparative negligence," in which a judge or jury can figure out that an accident was the fault of one or more parties. For example, a jury could say an accident was 80% one persons fault and 20% another persons fault, thus decreasing possible damages awarded by the percentage of liability. Say your damages are $10,000 and your found to be 20% liable, you only get $8,000.

Virginia does NOT use "comparative negligence" but rather "contributory negligence." Contributory negligence is a doctrine that states if you contribute at all to your injuries, then you can't recover a thing.  But don't automatically assume an accident is your fault.  Most people can't tell exactly what happened when they've been in an accident, so don't let the other driver guilt you into admitting anything.