Swollen and sore cuts.
 

I have a few swollen and sore cuts. I've cleaned them out with soap and water. Should I clean them out with alcohol or have them checked by a doctor? I don't know weather they're infected. Any advice?

If you are worried about them then it would be best to see your GP, common indication of infections are, sore, swollen, increased reddening, weeping, puss.
Generally using soap on wounds is not a good idea, even PH neutral soaps may still contain substances which may irritate the wounds. Warm water should suffice. There are products on the market specialised for cleaning open wounds. However having them checked by the doctor would be a sensible idea