Mountaineerfan. The queen must be mated if you see eggs. Unless you have laying workers. In the case of the laying workers you will see several eggs in a cell, the laying workers' abdomens are so short that they can't reach the bottom of the cell and "stick" the egg in the centre bottom. YOu should look to see how the eggs look. If they are in the centre, standing straight up basically, a queen has laid this egg and it could be your queen that you saw walking around that laid the eggs. After emergence from the cell it takes about 2 weeks for her to begin to lay, she may have emerged over two weeks ago, unless you know differently. Good luck, let us know what you see and find.
Don't kill this queen, make a split, like Kathy said, if you can. Beautiful life, great day, great health. Cindi