Can a urine infection get better on its own without antibiotics ?

Not infection: A true infection (bacterial) will not. You can get irritation, especially from certain dyes in certain drinks and other sources which will clear up by eliminating the cause.

Unlikely: Some infections in the urinary bladder, especially in patients with indwelling catheters, remain silent but persist. Sometimes they clear when the catheter is removed. If an obstruction in the kidney(example=a stone) is removed an infection may clear with strong fluid intake and a flushing out effect. Most urinary infections, except very mild bladder ones, require antibiotic therapy, however.