Pet shop remedies generally don't work very well, if at all.
Dogs with itchy skin can be incredibly difficult to diagnose, and often to get a proper diagnosis multiple tests are needed. Full diagnosis may take 10 weeks to complete, and that's only with a very systematic approach.
Bichon frises and other small dogs are notorious for getting itchy feet due to allergies - maybe to food, household allergens (e.g. dust mites) or outdoor allergens (like pollens).
Also a possibility is atopic dermatitis - another form of allergy (which the bichon frise is also more likely to have) which can only be diagnosed by exclusion - once everything else has been ruled out. This is why it can take ages to get to the bottom an itchy condition.
Once parasites (fleas, mites, lice), fungal infection, bacteria and allergies have been ruled out the chances are yur dog has atopy.
Some people say fatty acid supplements may help, but ask your vet to be sure. Let us know how you and your dog get on.