Could a pain in my side be due to my baby lying sideways in my womb?

Maybe. This is a possibility but you would/should be able to feel if the little one has turned sideways since it will tend to be a bit more painful than a simple ache.
Yes. Posiitonal changes during pregnancy can be experienced by you as the baby turns and rests on one or another side of your abdomen. If the pain is persistent and the it does not shift as you change positions, this needs to be further evaluated. Enjoy your pregnancy and all the movements that you baby will have you feel.