Why limit yourself to a mere AM radio when you can get a radio that has AM and SSB?
Who says you can't have both?
A Cobra 142, 146, and 148 GTL are plentiful and fairly inexpensive too. Very popular for fair reasons; their receive is xlnt and so is the transmit. Little to no freq drift on SSB; a big plus.
A Galaxy radio will drift a bit on SSB until it warms up. These are also very popular radios too. Some people like the transmit audio of the Galaxy over a Cobra.
You didn't say what kind of antenna you have - or if you use a Low Pass filter. These items can make a difference if interference is an issue. A Low Pass filter might cost a few $$ for a decent one; but worth it.
Low Pass filter at Copper Electronics (lowest price/highest grade CB filter):
Copper Electronics, Inc.
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Review of the same filter:
RF Limited DF3000 Low Pass Filter Review
Some antennas throw off more interference than others, such as an Imax 2000 or a Solarcon A99. The Maco V-58 might help. It is a bit more difficult to assemble than the A-99 or the Imax; but it is easier to control 'common mode current'. Now, common mode current can make a difference with interference too; both to you and others around you.
A bit technical I'll admit, but this happens quite often. Hams and CBers both can have this problem, but there are solutions.
Antenna height can make a difference too. Antennas mounted higher up will also have less 'fundamental overload' to consumer electronics.
EDIT:
Ground your equipment too. That is a 'must do'.