Can I still file a claim if the accident was partially my fault?

Yes, unless you are mostly at fault.  Frequently, there is more than one factor contributing to an accident.  Thus, the law allows a person who is partially the cause of his or her own accident to file suit against the person or company who is primarily at fault.  However, your damages will be reduced by the percentage of your fault.  For example, if your damages are $100,000 and you are 30% at fault, then your claim will be reduced to $70,000 to account for your own fault.  If the case is settled, then the reduction is a matter of negotiation.  If a jury decides the case, then they determine the percentage of fault for each party.