My baby(dog) just finished drinking water and eating, now he keeps gagging like he needs to vomit but can't!! What to do?

Sometimes when your dog is gagging frequently, there may be an infection or another problem that is irritating the pharynx.
Anything that produces a lot of mucus, from viral infections to allergies, will often cause dogs to gag.
Some pets have anatomical peculiarities that make them more prone to gagging. Meaning it's just like a defect of sorts in their throat.
Some dogs have extra tissue at the back of their throats that can be very irritating to them.

This part here is copied and pasted from Pets Symptom Solver Tool -- Mouth, Nose, and Teeth

See Your Vet If...

Your pet gags only when he is on a leash

Your dog is coughing as well as gagging

Your cat is coughing up hair balls

Your dog or cat has a runny nose and scratches frequently

Your pet can't open his mouth or is having trouble opening it

He can't close his mouth

He won't eat or has difficulty chewing or swallowing

His tongue, lips, or muzzle are swollen

There is a foreign object stuck in his mouth

His gums are red and swollen, or there is bleeding

Your pet is drooling or panting excessively

His tongue or gums are blue or pale

Your pet has ulcers on his tongue

He is gagging frequently

There is a lump anywhere on his face

He is pawing frequently at his mouth or face

There is a discharge from his mouth or nose that lasts two days or longer

His breath is consistently bad

Your pet's nose is dry, crusty, or bleeding

His mouth is foaming, or he's grinding his teeth

There is dried saliva around the mouth