Can positive covid test actually be false-positive and actually be acute HIV infection?

2/10 - I had unprotected insertive anal

2/11 started pep after 19 hours

3/12 finished pep, took all doses on time

3/19-3/23 - mild sore throat, cough, runny/stuffy nose, headache, temp max of 99.4 (family members also sick during this time)

4/2 - headache and mild sore throat, temp max 99.4 return. also have tingling/pins/needles/mild burning sensation throughout body. rapid/PCR test is positive for covid (family members also sick but tested negative for covid)

These symptoms started after pep course ended so this is ARS right? I read that PEP can delay seroconversion and ARS as a result.

Can covid positive actually be due to cross-reactivity with acute HIV and in fact be false-positive for covid but picking up acute HIV? Some studies below show this can happen.

The fact that my rapid covid test is positive but family members is negative leads me to believe this is ARS. https://www.sciencedirect.com/science/article/pii/S1341321X21001185

I did a PCR covid test yesterday and waiting the results. If the PCR is positive, does it mean the symptoms were definitely caused by covid? Also, how could I be positivie for covid but family in close proximity tested negative?

I know I have to go and test. What is the chance that pep failed?

Recent COVID-19 Can Confound HIV Test Results

False-Positive Screening and Confirmatory HIV Diagnostic Test in a Patient with Cured SARS-CoV-2 Infection Is Not Mediated by Env/Spike Cross-Reactive Antibodies - PubMed