Swim before (one's) eyes verb phrase
This phase is often used to describe the phenomenon of seeing light without light actually entering the eye, called phosphenes
If something swims before your eyes, it appears in your vision or clouds your eyes.
If you usually see floaters swimming before your eyes, you need to have consultations with doctors.
After hours of studying mathematics, Tom could see nothing but numbers swimming before his eyes.
Suddenly I felt sick and short of breath, and flashes of light seemed to swim before my eyes
The verb "swim" should be conjugated according to its tense.
If you swallow the bait, you take something that someone offers you, or agree to do something that someone asks you to do without knowing that it is a trick or way of getting something from you.
You can't just do whatever he wants you to do. Don't swallow the bait.