What can I do if I poked my eye with tweezers?

In pain?? If your eye is seeing well, and you have no pain, and the eye looks normal, you probably don't need to worry. Otherwise, go see an eye doctor. You can use artificial tears in the meantime to soothe your eye.
Exam. If you sustained a corneal abrasion or scrape to the eye, it would be painful, watering, red, and difficult to open. Otherwise if it resolves quickly, then probably just a minor irritation that can be helped by lubricating with artificial tear drops.