95 Cavalier..Eng light on plus oil pressure light on

I need some advice. The check engine light is on plus the oil pressure gage is on in my 1995 Cavalier. It has had an oil change and a tune up recently. It has 160000 miles on it...the engine light comes on after about 10 miles then if I drive more the oil pressure light comes on when I stop. The car sounds fine and it is not running hot or anything although the temp light does go on the high side once in a while. What could be the problem? Please advise. :eek:

could be the oil pump