You won't ever get given it again because you will have this severe reaction written in red very large all over your records and you can consider wearing bracelet or even getting a tatoo. This is the sort of thing that should be mentioned whenever you are giving your health history. Make sure it is noted on your GP's records.
In fact when giving a health history every single thing should be mentioned including ob/gyny stuff even if you think it is irrelevant. Something like an ingrowing toenail probably wouldn't have any relevance, but I am sure you get my point. Of course in any decent medical practice in normal circumstances you are asked about allergies. You will also mention it everytime you are given a prescription and to the pharmacist when you fill a prescription.
There is no point in badmouthing the NHS because this sort of thing happens all over the world in all healthcare systems and in first rate private practice too because there is no way of telling who is going to have an allergic reaction. Thousands of people take these drugs without any bad reactions at all. There unfortunately has to be a first time.
I could not ascertain that trimethoprim is in fact by itself a sulfanomide antibiotic. It was certainly used along with one in Bactrin and Septrin for example. If you get those brands there would be no way of telling if it was the trimethoprim or the sulfonamide you were reacting too. It's all quite complicated and I might have misunderstood it. See the link below
A bad reaction to sulfonamides is especially common in people with lupus. It is so common that it figures on the St Thomas list of so called Alternative Criteria. The top lupus doctors recommend using alternative antibiotics whenever possible.