Given the data you provided (frequency and urge to urinate accompanied with pain, no leakage, no infection), you might be experiencing a neurological disorder affecting the nerves associated with the bladder. What kind of neurological disorder might be present, cannot be determined without an additional examination (physical examination, X-ray or MRI of the spine).
You might want to visit a neurologist to check the nerves responsible for the bladder. Examining the lower lumbar and sacral part of the spine might be needed, because the nerves actually start from there and the cause might be located in the spine.