if the transformer has a rating of 3A, does it mean the maximum safe current draw from center to right is 3A? What if I'm not using the center and instead, I'm using left and right terminals (using fullwave)? Is the maximum still 3A? thanks
Are you now using it with a bridge rectifier across the full winding, ignoring the center tap?
You can make certain measurements to determine if you are overloading the transformer. To make them, you need a meter that can measure true RMS amps. Do you have such a meter?
The 3A is the current rating though the winding, either from end to end or end to center-tap. But that's an RMS rating and is more than the DC filtered current you can draw from a rectifier connected to the transformer. That is due to the high peak currents that a rectifier and filter draw, which causes the RMS current level to be above the DC current level.