I don't know about
Rosacea, but 2 of my friends who were bit by ticks got the butterfly rash. So I think Rosacea can be a possibility. One friend got several Bells Palsy and the butterfly rash which flares up whenever there is a stressful situation. She's been on steroids several times, which worsened her condition. She is only doing herbals now and she was never given abx for her issues and she has never been treated for Lyme, although she has all symptoms of late stage lyme.
The other friends leaves in a tick infected area. THey are everywhere on his property. He had a couple of psychotic episodes and he has been put on anti-psychotic meds but never tested for Lyme.
They both leave in Europe in a country where Lyme is even more of a headache than here, when it comes to doctors + testing is very poor.