Firstly, you shouldn't be finding y in terms of x, you should be using the standard parametric formula dy/dx = (dy/dt) / (dx/dt).
Secondly you have created a problem for yourself - because t can take on negative values and y = 3sin t, it is possible for y to be negative. But when you write y = (something)^(1/2) you are choosing the positive value of the square root as that is the convention for both the square root symbol and the power 1/2 (otherwise you wouldn't have a valid function). Therefore you need to be really careful when manipulating parametric equations.
(Note: you could write x in terms of y^2 and use implicit differentiation if you have covered that. That would eliminate the problem caused by taking square roots.)