I found an excerpt from here.

It looks like he went out with his 先輩{せんぱい} for the first time drinking, in which he never drank before and felt very nervous.

Then his 先輩 says:

その代わり笑わしてな。でも、俺が真面目に質問した時は、ちゃんと答えて

So he feels under a lot of pressure to make his 先輩 laugh, also they have a very quick exchange back and forth where he is under a lot of pressure to answer.

僕も吐きそうになりました

While a literal translation of this is "I feel like I'm going to vomit" I think a more accurate interpretation is "I feel sick". I often here this phrase in a situation where someone is under a lot of pressure too. For example, when you have a huge workload and you don't know what to do next, I would hear this phrase from a co-worker.

I found an excerpt from here.

It looks like he went out with his 先輩{せんぱい} for the first time drinking, in which he never drank before and felt very nervous.

Then his 先輩 says:

その代わり笑わしてな。でも、俺が真面目に質問した時は、ちゃんと答えて

So he feels under a lot of pressure to make his 先輩 laugh, also they have a very quick exchange back and forth where he is under a lot of pressure to answer.

僕も吐きそうになりました

While a literal translation of this is "I feel like I'm going to vomit" I think a more accurate interpretation is "I feel sick". I often hear this phrase in a situation where someone is under a lot of pressure too. For example, when you have a huge workload and you don't know what to do next, I would hear this phrase from a co-worker.