Did you warm up before training at all or you did, but not just before chin ups?
I'd do some bicep curls/ press ups before going chin ups if you can only do 2 at a time. The loads will be lighter and you will get some warming up before you load yourself up on the chin ups.
I hang up on the bar for a bit moving around to warm up my shoulders just a bit.
Which portion of your arm hurts? Could be a lot of different muscle strains, but as Koing said, you should be warming up before doing something you can only do 3 reps of. It's not a diss on you, but if you think about if you had to do a 3 rep max squat, you'd do some warm-up sets to get there.
Standing inverted rows, don't have to be perpendicular to the floor, just to get the blood flowing.
Chin ups palm down aggravated my bad tennis elbow (came from typing) which took 4-6 months to heal up. I had to do them palm up and cut down on the reps.
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