I would recommend asking your GP to do a full blood test, and get the lab to check for iron (both haemoglobin and feritin) red and white blood cell counts, vitamin D, B12 and folate.
My husband and daughters had covid in oct half term, and although I did have the heavy cold the week before that I repeatedly tested negative on lfts and pcr tests.
I phoned the GP at the start of Nov as I was really struggling with getting enough oxygen, feeling light headed, tight chest, dizzy, shaky and extremely fatigued. I got sent to the emergency care centre and then spent the whole day in A&E, had chest x ray and ECG, all fine. Only thing they did find though was extremely low iron levels - my ferritin was at 3, and it should be more like 80!
Over a month later, I'm only just starting back to work on a phased return starting this afternoon. Have had 3 ferrous sulphate (iron) tablets every dqy and am also supplementing with double dose of high strength Vit D, B12 spray and multivitamin drink with b complex.
The more Ive read about anaemia the more I've found that so many symptoms, not least fatigue etc, can bw down to that, but also that iron levels can drop significantly in response to fighting off an infection, so really need building up after. Also that the optimum levels are way higher than those deemed acceptable by nhs standards.
I have a referal this afternoo for an appointment to see respiratory consultant at the hospital to see what else we can nkw do ro further boost my energy levels and reduce the breathlessnes and lightheadedness, as I really want to back to my usual hours at worm in Jan.
Hope the GP is helpful, Ive really had to convince my to test for all the right things, not just be fobbed off with 'its post viral, just rest'. Ask for a print out of the blood test results too.