Hi, I am 19 years old and recently I have been having trouble with the right side of my jaw. It doesn't feel like painfull just like it is constantly sore. Also my jaw pops when I chew food or gum on the right side of my mouth. Please let me know if you have any knowledge on this subject.

You are probably clenching and grinding your teeth through the day and night. You should see your dentist so that he/she can assess it properly for you. You may need to wear a night guard when you sleep to protect your joint. I'd suggest that you give up the gum chewing until you know what is really going on. I am sure the gum isn't helping matters.

All right thank you, what exactly does a night guard? And what does it do?

I have a similar problem and talked to my anatomy professor who is also a Chiropractor and told me to go to my dentist to get a night guard and then maybe make an appointment with a chiropractor- apparently they can do certain exercises to help it out depending on how severe it is. He even mentioned that some massage therapists know how to help it as well. The night guard will protect your teeth from the grinding/clinching that you're probably doing without knowing.

Grinding and clinching can cause the muscle there to become very tense and when you open can sometimes come too far out of the socket that your jaw is part of.

A night guard is made of a hard acrylic. It will either be made to fit the top or bottom teeth.
Here in Canada the cost is just under $400.00, most dental plans cover them.
The dentist will have to take impressions of your upper and lower teeth and should take a measurement with an instrument called a facebow (looks funny doesn't hurt). The impressions will go to a laboratory and in about 10 days your nightguard will be ready to pick up.

How long will it be like this if I don't see a dentist, I am not saying that I won't, I'm just wondering if it will go away in time

It may go away, stay the same or get worse.
Avoid eating ANYTHING chewy or opening your mouth wide. When yawning keep the tip of your tongue behind your top front teeth to prevent opening wide.
You could try taking Ibuprofen and avoid sleeping on your right side especially if you sleep with your hand under your face.