my flight schedule is from guangzhou baiyun airport and i come from shenzhen and will stop at shenzhen east railway. is there a metro going directly to the airport?

No, no direct MTR is available between Shenzhen East Train Station and GZ Airport. I suggest you take a train at the train station and you may arrive at GZ Railway Station or GZ East.

If at East Station, it is suggested to take local subway line 3 or shuttle bus line 6 to the airport.
If at the main train station, you can walk to nearby CAAC Ticket Office to take shuttle bus line 1 to reach.