Your math does not sound right to me. If E=IR (ohms law) and W=IR then 10.83 amps x 12 volts = 129.96 Watts. If your real wattage is 65 then you're only pulling 5.41 amps. You also should base all your calculations on 14 volts, not 12.
I would recommend using at least a 20 amp relay for either headlight and possibly a higher rating if using halogens depending on the wattage given from the manufacturer.