Lights flashing on and off on dash

When I drive my car after about twenty minutes the oil light flashes on saying ‘oil pressure fault stop now’. About five minutes later my temperature light comes on and the dash says ‘temperature fault stop now’. They don’t stay on permanently they little flash on and off along with the bleeping noise. It seems to happen mostly when I’m stopped e.G at lights. I’ve checked my oil which is fine, also checked which seems fine, but I do feel it drains quicker than it usually should, I put water in it every other day. Does anyone have any idea what these problems could be? Could it be my sensors are on the blink? Or something more sinister? Thanks in advance.