*Linear* power supplies that don't pass basic EMC. On the plus side, when it burns out a few months later, you'll be older and wiser, and shopping for a unit that's actually worth the money you'll pay for it.
Conversely;
I don't know what your transmitter is doing, but it's doing it wrong. There should be no common mode current coming back from the antenna. "Duh" cases where this will happen: 1/4 wave 'whip' with no ground plane, any balanced antenna type (e.g., dipole) driven unbalanced.
If what you built is the dumb old two transistor oscillator circuit, you can try putting a tapped coil on the output, instead of a single one; and connecting equal length antennas to both sides, so they get complementary voltages. This is a basic dipole + balun.
Tim