testing tells the truth about having HIV
usually do not. Even with the most classical symptoms, ARS is a less common cause than other viruses, even in people at high risk, and you are correct that absence of rash and lymph node enlargement argues against HIV. Although colds and flu indeed are most common in colder months, they are not rare in the summer.
In any case, you need HIV testing to know for sure, and you should not wait to do it.