I poked my eyes. Is there an antibiotic that I can put on really quickly to make my eye heal faster?

See an eye doctor. Injury to the eye can be more severe than it seems. A scratch may become infected, requiring prescription antibiotic drops. Additionally, the eye can become inflamed, and steroid eye drops may be necessary. You would need an eye doctor to evaluate and treat this appropriately, and quickly. The sooner you are treated, the greater the chance your eye will heal properly.
Yes. You should see your ophthalmologist for an exam. You could have a conjunctival or corneal abrasion, which would need to be treated with an ophthalmic antibiotic ointment.