1 - Yes, it is possible for Lyme to lie dormant for a long period of time before you get symptoms. The second bite could have triggered the activity of the alread-present Lyme.
2 - Skin sensitivity could be a die-off reaction (herx) caused by the antibiotics...or could be a symptom of the Lyme infection itself.
Check out the thread at the top of the forum titled, "The Basics - Newbies, check this out!"
Chronic Lyme Disease, Gluten & Sulfite Sensitivity, Many Food/Inhalant/Medication/Chemical Allergies & Intolerances, Asthma, Gut issues (dysmotility, non-specific inflammation), UCTD ("Secondary Lupus-Like Syndrome"), Osteoporosis, Pancytopenia, chronic malabsorption/malnutrition, etc.; G-Tube; Currently TPN-dependent.
Meds: Zofran, Pulmicort, Heparin (to flush PICC line), Claritin, Colloidal Silver (used topically), IV Milk Thistle, probiotics.