Hi,
I came to US one year ago by J1 viza, then I changed this viza to F1. Now, I am on CPTraining. Am I allowed not to pay Social Security and Medicare taxes?

Yes, you ARE exempt from FICA (Social Security and Medicare) taxes while on CPT.

The duration of the exemption is the period while you are under the J-1 or F-1 visa, or five calendar years, whichever is shorter.