Engine noises

We have a 97 Civic LX with around 87K on it. within the last few months the engine has been making this slight rattling tapping noise when accelerating around 2000-2500rpm but has happened in other rpm ranges. When it first started it sounded horrible like something metal was loose and shaking inside the engine. I found out the car was low on oil. I added some and the noise quieted down a lot but was still there. It seems to come and go randomly. It sounds to be coming more from the driver side of the engine. the noise sort of reminds me of a lifter tap. As anyone else experienced this?

Adjust your valve clearances.