humabrom, have you tried the Simple range? You can get it at any high street pharmacy like Boots. Tesco used to carry it as well. From what I remember Oxy 10 can be fairly harsh on the skin. It may be better to try a gentler hypoallergenic range instead.
I'd suggest you go to Boots or any chemist store or pharmacy counter. Ask to speak to the pharmacist and see what they recommend you try (not just the counter assistant). Chemists are great for recommending products, especially the small private ones. I used them many times instead of going to the dr.
Don't rule that out though! Your doctor will help you too so consider making an appointment. They may feel you need a prescription based medication rather than an over-the-counter treatment, so why not give them the chance to assess your needs.
For blackheads on the nose, Biore makes pore strips which are specifically for that. I've used them myself and they were great. I know you can get pore strips in the UK because I did when I was there but am not sure if it was that brand. Again, try Boots or Tesco. I was a big Boots fans when I was there. Hope that helps!