Well eczema comes from gut problems. You most likely have gut dysbiosis. Those bumps on your skin possibly come from a viral infection think chicken pox, herpes or any other viral skin infection that causes bumps and rashes.
When you have lyme you also have viruses/bacteria/fungal infections along with heavy metal accumulation. This is because all of those items are controlled by the immune system(methylation). Try researching methylation and take methyl supplements to boost your immunity against infections and also to boost your heavy metal excretion so you heal faster.
Taking antibacterials causes viruses and fungal populations to increase. Your getting a rash because you probably knocked down some bacteria with meds and caused viruses to react.Viruses/bacteria/fungi have a balance and when you decrease one of them the other increases.
Candida only goes away once heavy metals are reduced. If you kill candida it will just come back but what keeps it down is ; nystatin, goldenseal, caprylic acid, Wormwood or any other medicinal herb(antifungal/bacterial)