I had a similar situation, and definitely had anxiety, but I absolutely do not believe that explains everything. I had a temperature of 99.5-100.5 for several months after having "recovered" from covid, and none of my doctors believed "psychogenic fever" was a valid thing.
In my case, I'd been dealing with anxiety my whole life, but it never caused physical symptoms. Then I had covid, felt better for 2 weeks, then suddenly started experiencing low-grade fever, night sweats, fatigue, no appetite inability to sleep for days on end (this was the worst. would feel like I stopped breathing whenever I started drifting off, and it felt like my body would then jump-start itself and violently kick me back awake). None of my doctors knew anything about long covid, and I started to wonder if I was dying of cancer or something. The symptoms were distressing enough to make anxiety a logical response. So, yeah, at some point, anxiety probably created additional symptoms, or made me more distressed by my symptoms, but neither I nor any doctors I've met believe anxiety can cause a fever, at the very least.
In my case, I'd been dealing with anxiety my whole life, but it never caused physical symptoms. Then I had covid, felt better for 2 weeks, then suddenly started experiencing low-grade fever, night sweats, fatigue, no appetite inability to sleep for days on end (this was the worst. would feel like I stopped breathing whenever I started drifting off, and it felt like my body would then jump-start itself and violently kick me back awake). None of my doctors knew anything about long covid, and I started to wonder if I was dying of cancer or something. The symptoms were distressing enough to make anxiety a logical response. So, yeah, at some point, anxiety probably created additional symptoms, or made me more distressed by my symptoms, but neither I nor any doctors I've met believe anxiety can cause a fever, at the very least.