Is it possible to give myself herpes from masturbating?

No. The herpes virus is spread by contact, usually skin to skin. There is a very slim chance if contracting the virus from sex toys that have not been cleaned and have fresh mucous on them, such as with mutual masturbation, but otherwise no.
Yes! Herpetic whitlow is herpes simplex of your finger- common amongst health care workers before gloves and on thumb suckers. If you can get it on your finger then u can transmit it to your genitals- even more so if using your saliva for lubrication.
Unusual. Maybe if you had a fever blister and cross-contaminated topside and bottom. Otherwise, you would have to be exposed to the virus somehow or someone.