As both the symptoms and treatment (if any) of dysphagia range from momentary to lifelong it really is not possible to break down treatment timelines in anything but the most simplistic fashion.
When surgical treatment is indicated it is better to discuss your personal situation with your treating clinician.
For lifelong severe forms of dysphagia, food intake may have to be non-oral (temporarily or permanent), or may be oral with often modified food textures, or a mixture of both forms of feeding. Speech and language therapy have a long-term role in the assessment of swallowing and in providing training for safe swallowing manoeuvres.
When medical treatment is being used, for example, a trial of an acid suppressing drug (usually a proton pump inhibitor and an alginate), improvement in symptoms would be expected within a week. You should not simply persist with unsupervised medical management if symptoms persist using these medicines after two weeks.