For a while now I've had a problem with my right forearm. It gets very tired then tense and just doesn't seem to go away. I'm an engineering student, and it seems to start bothering me when I have to write out a lot of equations.

Up till now, I've never really had a problem with this, just annoyance, but I noticed today that the tensness seems to be slowing down my jabs. I fight in a southpaw stance. I'm wondering if there's anything I should be doing to try to relieve the tension.

May I ask where about is the pain you are feeling in your forearm. And what kind of pain would you describe it as?
The best thing to do is start doing some light stretches for your forearm as this will help you arm and also boost flexibility.
Try the following:

Inside forearm stretch:

1. Grasp the fingers of your right hand with your left hand and pull towards you (right palm facing away from you)

2. Slowly raise the height of your arm to your head height.

3. Slowly lower to belt level.

Outside Forearm Stretch:

1. Grasp your left hand with your right hand placing your right thumb against the back of your left hand.

2. Twist your right hand counter clockwise by pushing with your right thumb and pulling with your right fingers.

It’s quite hard to understand without pictures although just look up the stretches on Google and you should find something.
Remember to go easy at first to see if your forearm can cope with it. Good luck and I hope these help.

It's located on the inside of the arm, on the side with the pinkie and ring finger. It sort of feels like I'm working the muscles too hard, not giving them enough time to rest, and they become to tense as a result.

With that inside arm stretch, should I be keeping my arm straight out the entire time, and try to keep the palm completely vertical as I lower the arm?

If it is being caused by overworking those muscles, will strengthening my forearms help, or just make them more tense?

Yes with the exercise keep the arm straight out the whole time as you will feel the stretch more and it is more beneficial. Remember if you are going to do this please take it easy at first as you do not want to damage yourself.
As for strengthening your forearms it will help to some extent but dont overwork them. The pain could be caused from something you are doing wrong in your training, for example when I trained I used to get pains in my elbow and later found out it was due to me doing something wrong. Just a thought.
Hopefully this all helps.

Here's something that may help...

Sword work, Tennis, and MA all have something in common. Tennis elbow. Which can have the exact symptoms you have described, It can get worse as well. In tennis and sword work you can increase your grip size and get physical therapy and massage to help. In MA you can make sure your puches do not go to full extension and if they do, then pull back a little at the end and don't hold the punch at full extension. Also, get some therapy or massage. I've had this before and it can also seem as if your grip strength as well as wrist strength can go. You can also test this by using your thumb with preasure right on your forearm muscle near your elbow. Not on the bone but the muscle. Classic tennis elbow should be inflamed tight and Very painfull. If this is the case, stop and seek therapy. You can also help by using tape to increase the size of pen or pencil in order to make the grip larger or buy one of the many new ones with a much larger grip. I hope this helps and can give a possible name and even possible solution to your condition...