One finds it easier to keep the wounds clean and use less topical medication after cutting the hair short or shaving it.
A non-Sikh doctor would generally advise you to do so.
You need to analyze why you would agree to cutting your beard after just 10 days of a messy rash. When we value our hair we gladly accept various inconveniences due to our hair and we regard them as normal, a part of our life.
I am quite confident that the length of hair is not the cause of your rash, nor is it an impediment to its treatment, even though hair over wounds can be quite annoying. But it is too soon to rush to a barber.
You may have an infection or, reaction to some cosmetic, hair gel etc. Try to have your doctor find the cause of your rash that started after your coming to UK, rather than just treat it, so that it does not recur in the near future.
With proper treatment, perhaps a course of oral antibiotic, something that started only 8-10 days ago, should not take long to clear up.