It is definitely possible to have pulp (the nerve of the tooth) damage in the absence of decay.
Other causes of pulp damage/inflammation include:
1) Cracks in the tooth or root
Hairline cracks may be present in the crown or the root of a tooth due to trauma (from an accident, teeth grinding or clenching, or biting into something hard) or weakening of an undermined cusp usually associated with a large cavity or a large filling.
Most cracks may be painless when confined to the superficial part of the tooth. When a crack line starts to extend deeper into the tooth, thermal sensitivity and tenderness on biting may develop. In severe cases, the crack may communicate with the pulp and cause the pulp to die from the chronic irritation caused by bacteria entering the crack.
Many crack lines are invisible on xray and can be challenging to detect. There are methods to visualize and detect cracks such as removal of any existing filling material to check the cavity floor, transillumination, and bite testing.
Root fractures which occur under the gumline may sometimes be detected on 3D xrays (CBCT scans) or when an exploratory gum flap is opened to visually inspect the root surface.
2) Inflammatory root resorption
This means that the root of the tooth is being eaten away by immune cells within the bone, usually in response to trauma. The affected tooth may be loose, the crown may have changed colour and there may be a gum pocket communicating with the resorptive site.
Root resorption has a characteristic appearance on xray in the late stages. Early stages may be detected on CBCT.
3) Teeth grinding (bruxism)
Overloading of the teeth and supporting structures during bruxing may cause poorly localised sensitivity and tenderness to biting. Some individuals also experience tension headaches (usually in the temple region) where a jaw muscle attaches to the skull. The affected teeth are usually healthy and this condition is temporary. Bruxism may increase your chances of developing a cracked tooth, so management of this condition is essential for maintaining a healthy set of teeth in the long term.
4) Referred pain
Occasionally, patients may perceive dental pain when in reality, it is another non-dental structure (such as the maxillary sinus) that is the true source of the pain. As with bruxism, this diagnosis is based on the exclusion of dental disease (decay, cracks etc). Sometimes, the patient may be so convinced that the pain is dental in origin that they may request for unnecessary dental treatment (root canal treatments, extractions) to be performed, usually unsuccessfully because the pain does not improve. Careful examination and diagnosis is key. I have answered another question recently related to this topic here.
5) Pain syndromes
Even more rarely, patients with undiagnosed conditions such as trigeminal neuralgia may present with dental pain. These cases are usually managed by neurologists.
I would seek a second opinion if the pain is persistent to get it diagnosed and properly managed.
