CARGO PLT HAD TAXI CONFLICT WITH ACR ACFT.

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IN ORDER TO DEPART FROM THE MCALLEN MILLER INTL ARPT (MFE) TO LAREDO INTL ARPT (LRD) I RECEIVED A CLRNC FROM THE GND CTL TO TAXI TO RWY 13 WITHOUT ANY OTHER INSTRUCTIONS. I ACKNOWLEDGED THIS CLRNC AND STARTED TO TAXI VIA TXWYS D AND A TO RWY 13. I SAW AN ACR B737 SLOWLY TAXIING ON THE COMMERCIAL RAMP AHEAD TO MY R; ALSO TAXIING FOR DEP. I KEPT THE TFC IN SIGHT AND EXPECTED FURTHER INSTRUCTIONS FROM THE GND CTLR. DUE TO MY MISMANAGEMENT OF BOTH RADIOS AT THAT TIME I COULD NOT HEAR THE GND CTLR. BASED ON PREVIOUS CLRNC AND POS OF BOTH ACFT I CONTINUED TAXIING WITH CAUTION; PASSED IN FRONT OF THE B737 AND THEN CONTACTED THE TWR CTLR TO REQUEST A CLRNC FOR TKOF. THEN I LEARNED THAT ATC HAD TRIED TO CALL ME TO GIVE WAY TO THE B737 AND THAT THE CAPT OF THE B737 HAD CONSIDERED MY ACTION UNSAFE. I APOLOGIZED AT THAT MOMENT TO THE TWR AND TO THE CAPT AND RECEIVED A CLRNC FOR TKOF. I COULD HAVE PREVENTED THAT SIT BY QUESTIONING THE GND CTLR ABOUT THE B737. THEN I WOULD HAVE DISCOVERED THE RADIOS WERE NOT SET-UP AS I DESIRED THEM TO BE.