Can you swap shifts with each other?

The employer has what is called the right to manage, which means that the employer has the right to manage and distribute work in the workplace. This may mean that your employer decides that you cannot swap shifts with each other.
However, in the best of all possible worlds, the employer will be responsive and listen to the workers' views on the matter. So I advise you to have a discussion with your employer and point out the disadvantages of their decision. Hopefully, you can then come up with something that benefits both the business and you and your colleagues.