synthetic oil or cheap oil?

my car is losing engine oil and a couple of days ago the oil light stayed on a few seconds after starting and went off again today I dipped oil and it was low so added a couple of pints of ^ cheap " oil I had in a gallon can , after about 20 miles I sped up to about ninety on a long straight bit of road as it was 5am and no one about and the engine light came on and stayed on constant so I stopped and opened the bonnet , a smell of burnt oil and a bit of steam , checked dip stick and plenty of oil showing so I started engine and drove on , ok going up the gears but when engine revs dropped below 2000 rpm the oil light came on and stayed on and gear change up to increase revs puts it out again , I drove about 10 miles and have parked the car ,, has the cheap non synthetic oil caused this / or have I blown the engine ? thanks