Hi Vitaka!
Welcome to our side of the site!!
I would suggest that due to your medications (mainly Remicade), testing may not be successful, but if you would go to our "New to Lyme? Start here!" thread, it has symptom lists that you can compare to your symptoms and see if they fit.
In my opinion, anyone that has conditions that kind of require them to be on medications that suppress the immune system and suspect that they have tick-borne infections as well, need to be sure to see a very well qualified LLMD to get the extra help they may need to overcome these infections.
I think I like your Neuro though!
Is he Lyme Literate, meaning has he had training from ILADS (International Lyme and Associated Diseases Society)?
These symptoms combined with a recent tick bite are surely a concern though! Babesia often causes a lot of daily headaches for people and for me, they brought on a lot of migraines too!