As you suspect this can be a result of of a systemic allergy. It could be her food, the fertilizer.etc. However, it can also be a sensitivity to the thyroid medication, or thyroid hormone in her system. She may have an abscess of a tooth or tooth root that is sending bacteria into her bloodstream Any infection that starts in the mouth has the potential to become systemic and affect the coat and skin and the entire body.
The first thing I would do is have her teeth and gums evaluated. Then check her thyroid hormone level and see if her dose is correct or needs to be adjusted. If she is eating food with corn, wheat or gluten as fillers, she may have become sensitve to these. You may want to try a natural or raw food diet and see if she feels.better. Any allergy is going to show up on a dogs skin eventually.
There is also a possibility these legions are fungal in nature and started by her ingesting some of the fertilizer.
Vitamin E is an excellent homeopathic product and it can be helpful but it is unable to cure these sores by itself. I would bathe her in a soothing oatmeal shampoo or check the excellent product at www.revivalanimal.com after that apply the baby product desitin - which is zinc ointment to the lesions. Make sure she does not lick any off. In addition give her a teaspoon of plain yogurt every day. That contains acidopholus and will prevent yeast.
When you have her bloodwork checked you my want your DVM to do a skin scraping to rule in or out staph or fungus. You can continue to use the vitamin E as that will not harm her. Also give her a daily vitamin suppliment containing omega 3 fatty acids.
I understand that nothing is more frustrating then seeing a beloved pet suffer and feel helpless to resolve the problem. I hope I have given you enough areas to explore as potential causes. Please let me know if you still have any questions. I will work together with you to solve this problem and get your sweet girl on the road to good health.
Sincerest best wishes,