The blood test for checking possible allergens is not as sensitive as an intradermal skin test (which is the best method).
As for acupuncture or any other alternative medicine, Please show me some quality evidence (accurate well performed trial) that proves that acupuncture is beneficial for a skin problem. These may work somewhat for people as a placebo effect but they most certainly will not in people. They have shown people have responded just as well to sham acupuncture needles placed in random positions and not in the correct manner (not along meridian lines and pressure points) and also people will respond to toothpicks that don't even penetrate the skin suggesting any response is simply a placebo.
Alternative medicines are not as safe as people think. For example, traditional chinese medicines and herbs (which are given in raw forms and uncontrolled doses) can be overdosed and toxic. Not all herbs are safe especially to pets e.g lillies may be natural, organic, herbal etc but they will destroy a cat's kidneys. Also these herbal medicines have been shown to add ingredients like steroids (often at far higher doses than normally prescribed).
As for acupuncture being very safe. Known side effects include bruising, pain, dizziness, vomiting and nausea. More serious problems include infection (spread of viruses and bacteria) through the needles (especially if not sterilized properly) and worse still, damage to organs and nerves when placing the needles.
It has been known for lungs to be punctured by chest needles (causing a serious condition called pneumothorax). Also kidneys have been damaged when needles have been in the back and the brain damaged when placed at the base of the skull. People have even died from needles penetrating the heart!!