Your biceps like to provide assistance when performing exercises for the back, however if you use a pronated grip (or overhand grip)to do your back exercises it puts the biceps in a weaker position to help out. This forces the brachioradialis muscle, to pick up the slack and aid in assisting the bigger muscle group working. The brachioradialis muscle is located on the upper, outer part of your forearm, and based on the grip you said you used, and your exercise selection, and pain felt afterwards, it sounds like you could potentially have suffered a strain in it. You mentioned you just got back into doing pullups, so your brach muscles probably aren't used to this type of exercise stimulus. That said, in the short term doing more pull ups or other "such activities" wouldn't help the problem, it will just increase the strain on the muscles. Long term, doing more and more pullups will strengthen those muscles, but just make sure you don't push too hard and cause any injuries.
Other ways to strengthen the brachioradialis:
- Hammer Curls: If you have access to dumbbells, hammer curls target the brachs, biceps, and other forearm muscles. If dumbbells aren't around, look for something with a handle that you can use instead. Check out how to do hammer curls Demonstration
- Reverse Grip Curls: These can be done with dumbbells or a barbell. Demonstration
- Farmer Walks: Want an easy way to get stronger forearms? Carry something that's heavy! Farmer walks are great, but if your not one for cardio, even just picking up something heavy and holding onto it for as long as you can will strengthen the forearm muscles. Demonstration.
For advice on recovery, I felt a physical therapist is really the person you should be asking, so I found a youtube video of one, talking about how to treat the exact problem it seems like you have now.
I want to also add that by switching to an underhand grip or supinated grip to perform your back exercises, you put the biceps in a stronger position, which means you won't be recruiting your brachioradialis as much.
Wishing you a speedy recovery!