Yes you can ease the stomach pain at home itself. This is known as cramping. Cramping in early pregnancy is common. You can heal the pain by keeping a heating pad or an electric heating pad on the stomach, but make sure it is not very hot, but is warm enough to ease out the pain.
Take care of yourself by getting plenty of rest and eating right. The changing hormones in your body can slow down digestion and make you constipated, which can cause abdominal pain. If you feel that you may be constipated, increase your fiber and water intake.
Another way to help relieve cramps in pregnancy is to abstain from sex. Sex does not hurt you or the baby but may increase the cramping and cause some spotting. The combination of cramping and spotting can make you think that you are having a miscarriage.