Assuming the conversation was about work, an example might be the following: I wanted to go to my son's baseball game, but right at the end of the day, I got slammed [with work.] My boss asked me to finish a report, I had to attend a last-minute meeting, and a conference call went overtime. I missed the game. [note: depending on the conversation, you might or might not include "with work." It's not a grammatical thing, more of a judgement call in the moment.
In my opinion, to get hammered refers to drunkeness. For example, "I got so hammered at the bar last night that I woke up in the alley with no pants." You would not say "I got hammered WITH alcohol" the same way you *might* say
I got slammed with work." I suppose you could say, "I got hammered ON tequila" (for example.)