I have been suffering from terrible nausea (but no vomiting) - my doc had prescribed me ASIC which is a form of antihistamine according to him.
I take 1 at night (he said to take 2 but the one helps me just fine!) It has helped my nausea tremendously!!! Only thing is it absolutely drains me of all energy. I have literally had to stay in bed until 5pm on a few occasions.
To answer your question, I asked my sister who is a paediatrician about the tiredness on these tablets, and she told me that a common side effect could be drowsiness or fatigue. How severe prob depends on dosage and the individual.
On another note, I missed taking the darn little nausea pill one night, and I was up early with a normal amount of energy but felt absolutely like I wanted to puke my guts out! TMI sorry. So I took the pill in the afternoon and got relief after a little while, but started to fall asleep on the couch lol
We can't win either way it seems with these third trimester blues - just gotta wait it out I guess!