Why you shouldn't eat before working out

When you eat, your blood goes to the stomach to carry away nutrients from the digestion of food and store it for use later.

When you work out, your blood is diverted to your muscles to carry away wastes (like CO2) and bring in oxygen and fuel.

If you do both at the same time - your body considers the muscles more "mission critical" and leaves the stomach sitting there holding its contents instead of digesting them... where the food rots instead of getting taken up as fuel. 

The prime window for a workout is about 3-4 hours after your last large meal (which should also land you in prime position for the next meal as soon as you are DONE with your workout.) If you eat directly after your workout, your fuel stores depleted during the workout are filled first (meaning it's not stored as fat.)

If you feel like you need some pre-workout energy you can have a small snack at least 30 minutes to an hour before.

So when your mom said you can't go swimming directly after eating, it was likely this reason at the heart of the origin of that rule (although she may not have known this concept and had likely made up another reason - like that it would give you a cramp.)