No. Gonorrhea can only be transmitted by sexual contact. So unless you were having sex with someone who is infected in the pool; you are free and clear. If you are that bothered, then go to your doctor and have a test done. If you are collage student, most student health clinics due STI testing for free, or you can go to Planned Parenthood but I think they charge a small fee for testing.
No you cannot. That's what the chlorine and stuff is for. There are many places to go for free testing if you need it! ♥