I am trying to install a eiko 44348901007 H3 55.

Are you sure that is the correct bulb for your car? Does it look the same as the one you pulled out? I am not totally sure but I believe your car takes an H4 bulb for both high and low. If I am wrong, when you pulled out the old bulb it would have had a wire on it as well. You would have had to disconnect it from a lead with a connector that fits the connector on the bulb wire. If this came loose the headlight would not have worked prior to now. If the lead is loose and the headlight was not working, there is the mating wire with the connector on it near the headlight bulb coming out of the harness.
If you need guidance to see where the wire is coming from or if you have the right bulb, look at the other side to see what you are looking for to connect the wire to.