[papajam]

Yes, it's possible that two bulbs can burn out at the same time but it's pretty rare. Voltage spikes can cause burn outs too. I'd check alternator output voltage. If it's more than say 14.5 volts, the voltage regulator may need replacing.
A relay is simply an electromechanical switch. It does not offer the load any protection from overvoltage. Fuses offer no protection from overvoltage either. Fuses protect the load/circuit from excessive current (amperage).