Whether to get vaccinated with a minor complaint comes down to how unwell you are.
Minor illness usually doesn't stop you
A mild cold, sore throat or runny nose without fever generally doesn't affect the safety or effectiveness of a vaccine, and you can usually go ahead. The immune system can handle a minor illness and a vaccine at the same time.
Fever or more serious illness means waiting
If you have a fever or a moderate to severe acute illness, it's generally advised to recover first. This is mainly to avoid confusing the symptoms of the illness with reactions to the vaccine, not because vaccination is especially risky.
People with chronic conditions
People with stable chronic conditions such as diabetes or heart disease are usually still suitable for vaccination, and often fall into the high-risk groups for whom it's recommended. If a chronic condition is unstable or flaring up, check with a doctor first.
Speak up before vaccination
Tell the health professional your current symptoms, any medication you take, and any history of severe allergy to a vaccine or medicine. They'll use that to decide whether the day is suitable or suggest rescheduling.