Health Benefits of
Mustard is a common name for three different species known as Sinapis hirta or yellow mustard, Brassica juncea or brown mustard, and Brassica nigra or black mustard. Mustard is one of the most important culinary ingredients after salt and pepper. The mustard plant originated in Western Europe, the Mediterranean, and Asian regions. However, the plant is also cultivated in North and South America and Australia.  The topical health benefits of mustard are listed down below.
Mustard for Psoriasis
Psoriasis is a chronic autoimmune skin condition. Mustard seeds improve erythema, scales, and skin thickness in psoriasis. These effects are achieved by suppression of infiltration of inflammatory cells, inhibition of the activity of enzymes, and reduced production and secretion of inflammatory mediators. Mustard seeds also act as antioxidants and reduce the levels of free radicals and reactive oxygen species, hence, protecting the tissues from oxidative damage. 
Analgesic Activity of Mustard
Inflammatory muscle pain can be alleviated from the use of topical irritants that rather active cutaneous nociceptors while suppressing muscular nociceptors. Mustard oil is a topical irritant that activates cutaneous nociceptors and relieves muscular pain, with a concomitant reduction in the activity of muscular nociceptors. 
Antioxidant Activity of Mustard
The antioxidant property of mustard is attributed to its constituent fatty acids that include oleic, linolenic, linoleic, and erucic acids in black and yellow mustard seeds. 
Figure 2 demonstrates the anti-fungal effects of different concentrations of black mustard essential oil on the fungal colony diameter of three different fungi. https://pubmed.ncbi.nlm.nih.gov/25836415/
Antifungal Activity of Mustard
The black mustard essential oil has antifungal properties when it is applied by either of the two techniques – direct addition in the liquid medium or vapor phase contact. Mustard oil contains sulfurous compounds that hinder the growth of fungi and produce both fungistatic and fungicidal effects. Allyl-isothiocyanate (AITC) is the most abundant constituent of black mustard essential oil that suppresses the biological activity of fungi. 
Mustard for Respiratory Tract Infections
Mustard seed footbath can provide relief to people suffering from pulmonary conditions that include chest cold or bronchitis and other conditions such as cold feet and hands.