You should have your brakes cleaned! Or have a mechanic look to make sure nothing is wrong. My neon does this and after driving a while it stops. Sometimes rust,dust and dirt particals get on the drums !!
Probably the belt.
it is possible to be the brakes or the transmission have it checked by a mechanic.
Frozen brake caliper
Haynes repair manual, Dodge Neon 2000 thru 2003. Book #30036
If the brakes works it will stop UFDA
DrumDrum
Never.
Alternator belt needs adjusting
Could have either on the rear. Both were an option.
Loose or worn A/C drive belt. Tighten or replace. If serpentine belt, replace.
That will depend on many factors including driving habits. The brakes could last 30,000 - 150,000 miles.
Assuming they are Drum brakes most likely the wheel cylinder is bad.