I Have Two Issues, Unsure If They Are Related. About

I have two issues, unsure if they are related. About 3-4 weeks ago the left corner of my mouth started getting cracked and very painful. Not a cold sore, almost like extremely chapped. No bleeding, but visibly cracked. I have tried numerous lip treatments (carmex, Burt's Bees, Chapstick), none helped. Thursday I tried a hydrocortisone cream on it. Nothing. Friday then I tried an antibiotic ointment on it. Again nothing. Saturday morning I tried a steroid ointment I have for my daughters eczema. Saturday night I was outside for the fireworks. Started getting a rash on my chin below the area I applied the steroid cream. I do not have a rash anywhere else, so I am confident I did not get into any poison ivy or oak, but the area on my chin/lip is red, swollen, itchy, weeping, and very irritated. Second, and unknown if related issue, is I noticed starting yesterday morning that under my chin, on the inside soft tissue just inside the jaw, is tender and sore. And now today there is a hard, tender lump in the middle. Is that my lymph nodes, and if so, could that be related to the rash?