This is not professional medical advice - so do keep your doctors appointment if you feel you need one.
Recall back when the rash first appeared, had you changed any washing products at that point? Has the rash spread or is it localised? Does it feel hot to touch or do you think it might be infected? If you think it is infected or you have a compromised immune system try and get medical help sooner.
It could be anything from mild eczema, psoriasis, dermatitis - a dry skin allergic rash to the perfumes and enzymes in clothes conditioners or washing powders, or any other cream, shampoo, or lotion you have in contact with your skin.
The cuts are your skins protective mantle breaking down. Keep hydrating your skin with 'no perfume' moisturisers and bob into a pharmacy to ask for the pharmacy advice. They might suggest a mild hydocortisone cream or heavy duty moisturiser.
Do a search engine image search under 'red skin rashes' and see if you can identify your rash. You can also look on the image results and see the advice for rashes or skin marks that you should get professional medical advice on sooner rather than later.
Hope this helps