The springs simply keep the quick release (QR) skewer centered in the wheel hub, making it easier to insert the hub (and wheel) into the frame dropouts. It has no safety function other than to facilitate seating the wheel correctly. If the wheel is not seated correctly in the drops when you tighten the QR then you run the risk of the wheel coming out during a ride. That said, this is true whether or not you still have the QR springs.
When tightening the QR, it should be tight enough that the QR lever leaves a mark in the palm of your hand.
Finally, if you are getting a squeaky metal noise your single QR spring may be on backwards, or as pointed out by Daniel R Hicks' comment, the two springs could have gotten combined together. First check to see that you only indeed only have one spring and that two springs haven't gotten entangled. When placing the springs back on the QR, the narrow end should point toward the hub, the wide end toward the end of the QR skewer. If the spring was installed backwards the wide end of the spring can get jammed into the frame and hub axle, potentially making a squeaking noise when tightening the QR.