Hi Steff and welcome.
Sorry to hear that your boyfriend is so sick. You're a good friend & partner to be hear on his behalf.
6 weeks of Doxycycline may not have been long enough. I have been on Doxy, 600mg per day, for 10 months. I started feeling better after 6 months of the drug.
I also have a co-infection of Lyme called Bartonella.
Did your boyfriend get tested for co-infections? The co-infections can complicate treatment.
I see a Lyme Literate Medical Doctor (LLMD) and it makes a huge difference. Other doctors I saw said there was nothing wrong with me and they poo-poo'ed my complaints.
I hope he gets to see an LLMD soon.
Peace and health to you both.