I had protected sex with my gf and the other day she got her covid 19 vaccine she is feeling nauseous and her stomach is aching it's been 4 days since we had sex is this because of the vaccine or she is pregnant?

Pregnancy related symptoms arise after the hormones of the conception are produced. Four days is much too early for these to be produced. These symptoms are something else, maybe the vaccine, maybe something different.

Conception occurs within day or so of the sex. It takes about 3 weeks for the embryo to make enough HCG for a positive pregnancy test. Blood test may be done a day after a missed period. Home pregnancy tests should be done 4-5 days after the missed period. If the result is negative repeat the test in 4-5 days. Use first morning urine and follow instructions for the test carefully.