Viral Infection: Many viral infections, such as herpes zoster (shingles), can cause a rash and imbalance due to the involvement of the vestibular system or due to systemic symptoms like fever and fatigue that can lead to dizziness.

Allergic Reaction: An allergic reaction can cause a rash and, depending on the severity, can also lead to systemic symptoms including dizziness or imbalance due to hypotension or anaphylaxis.
Neurological Conditions: Conditions like multiple sclerosis or peripheral neuropathy can cause both skin manifestations (rash) and neurological symptoms including imbalance.
Medication Side Effects: Certain medications can cause rashes and also affect balance, either through direct neurological effects or through systemic side effects.

Meningitis: Although less common, meningitis is a critical diagnosis that can present with rash (in the case of meningococcal meningitis) and severe imbalance or ataxia due to inflammation of the meninges.
Lyme Disease: Lyme disease can cause a distinctive rash (erythema migrans) and neurological symptoms, including imbalance or ataxia, especially in later stages if left untreated.
Sepsis: Sepsis, particularly from bacterial infections, can cause a rash and severe systemic symptoms including dizziness or imbalance due to hypotension and organ dysfunction.

Ehlers-Danlos Syndrome: A group of disorders that affect connective tissues supporting the skin, bones, blood vessels, and many other organs and tissues. Some types can cause skin hyperextensibility and joint hypermobility, potentially leading to imbalance.
Syphilis: In its secondary stage, syphilis can cause a rash and, in the tertiary stage, can lead to neurological problems, including imbalance, due to tabes dorsalis.
Vasculitis: Certain types of vasculitis, like granulomatosis with polyangiitis, can cause rashes and neurological symptoms, including imbalance, due to the inflammation of blood vessels.