There are a number of factors that might have influence on the blood alcohol content. However, in short, a liver injury is highly unlikely to increase the blood alcohol content. Although alcohol is processed in the liver, having a liver injury AFTER driving one or two beers would not necessarily INCREASE the blood alcohol level as the liver only breaks down alcohol, it does not sequester or release alcohol in to the blood. Depending on the extent of the liver injury, the blood alcohol might not decrease by as much as expected but it would most certainly not increase.
For reference, a 12 oz beer has about a 5-7% alcohol content. If a 140 lb person drinks it, (s)he would have a blood alcohol content of 0.03-0.04 after about 20 minutes and it would take about 1 hour to break down that alcohol.