Your code should work should work just fine. Golang is dead simple, there is no need for thinking about synchronizing read/write calls.
[EDIT] To be clear: Go's networking model is synchronous, just like any old style socket program. Go uses internally efficient tricks to deal with it but as a programmer you have the comfort to program sequential code, which is the whole point about goroutines. Goroutines can be like threads but they are so cheap that you can create a LOT of them (a.k.a. fibers).
Keep in mind that TCP might not send every piece in one shot. You should always check the return values to be sure that everything has been sent. Maybe the server just receives a part of the message and waits for more, but your client is already waiting for an answer? Just a guess.