Hello.
Thank you for your query at DoctorSpring.com.
I have the skin lesion and it looks like folliculitis (infection of the hair follicle). It tends to be painful but will eventually heal with the right treatment.
It is unlikely to be an insect bite, definitely not from a brown recluse spider. So do not worry about it.
Neosporin cream would have been the correct treatment. The reason why it may seem ineffective is because you have also used the cortisone cream counters it effect by boosting the infection, as it is a steroid.
I would suggest that you use the Neosporin cream alone, four times daily. Do this for a day and if there is an improvement, please continue the same till it heals completely. If not, you would require prescription strength antibiotic cream like Mupirocin cream.
If the pain is unbearable, you can take an OTC Ibuprofen 400 mg SOS.
I hope this was helpful. Feel free to ask queries.
Regards.