You can’t use a voltage divider for this type of load, and using e.g. a LM1117T would only give you ~800mA. And it surges a bit when it is powered up. Don’t feed 3V3 directly to the Pi. More likely the culprit is the 5V SMPS you are using to power the Pi, and not the regulator itself.
Use an LM350 to supply power... You may still get the 50/60Hz humming from your antenna, but it will reduce noise considerably. You can use sox (it will run on your CPU and cause a small delay on audio) to filter the humming, but a hardware filter is better. Google.
The LM350 accepts an input voltage up to 35V, can output 3A, and can deliver an output voltage of between 1.25 and 33V. It will enter a temporary coma if overheated, and really requires serious abuse before it dies. As a voltage regulator of the old school, it does require some heatsinking, but heatsinks are cheap.
It is best to keep the input voltage as close to the output voltage as possible, since the formula: ‘P_dissipate = ( Vin – Vout ) * Iload’ tells us that for e.g. (12V – 5V) * 0.5A = 3.5 watts must be dissipated. And that’s for the standard effect of a USB2.0 port, regulated down from 12V. For P_dissipate = ( 6.5V – 5V ) * 0.5 we get 0.75 watts, a more reasonable amount of wasted energy turned into heat, and that will easily be dissipated. In your use case, something like max 1.5A perhaps: P_dissipate = (6.75−5)×1.5 = 2.625W. Very moderate, considering that a current draw of 1.5A is probably not going to be constant. You can use a 40x40mm heatsink, but note that copper is ~3X times better than aluminium. This matters if you want to keep it compact.
Note that the 10ohm resistor in series with the trimpot is not necessary, nor is the momentary button and voltmeter.
To completely eliminate noise, you should also use a grounded metal casing, and a battery supply so your Pi is floating. But you’ll discover if it’s necessary.
If a LM350 does not fix your problem, you can buy an expensive power supply designed for use with audio equipment, as they have anti-hum/hiss/whine filtering in their designs. I am not into music, but then look for a SE forum for a recommended supply.
You should also shield your SDR in copperfoil and connect that to Pi GND. For the Pi itself, I recommend the FLIRC aluminium case, since it keeps my overclocked Pi very cool (it attaches to the CPU/GPU with a thermal pad, and radiates heat away). Here are a few eBay examples, which cost about the same as a FLIRC case: