Aspirin is both a pain killer and blood thinner that is used widely for both pain and prevention of heart attacks. There are no medications that are particularly safe to take when you drink excessively. With that said, aspirin itself will probably not damage your liver if taken in the recommended doses and without excessive alcohol intake. I think you may have heard that acetaminophen (ingredient in Tylenol) can damage your liver if taken in excess along with excess alcohol. There is some truth to this. If you drink excessively and consume more than 2 grams of acetaminophen in one day, there is a chance of liver damage.
I will say that I think that the amount that you are drinking should be cut down slightly. In general, the upper limit of alcohol a male can drink per day is 2 drinks or 1 drink for a female. If you are having more than this you should consider cutting down to prevent the long term damage alcohol can have on your body.
I suggest that you bring this issue up with your primary care physician
. He or she can examine your drinking pattern, make suggestions on how much to cut down, and discuss which medications are safe to take for pain when needed.