Yes it is possible to have nausea and mild cramps in lower abdomen following first intercourse , under the progesterone and prostaglandin released during the act of sexual excitement when can take 48-72 hours to come back to normal. This may present as frequent urination, mild uterine cramps , nausea and even headache sometimes .
These symptoms would subside on their own. In the meantime you may take warm fluids and use hot fomentation to soothe your lower abdominal cramps.
I hope i have answered your query,
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