I (M20) got sick about 2 weeks after sex. Worried I have HIV

About 1 month ago I started having sex with someone on weekends. And About a week or 2 ago ive started experiencing symptoms of being sick. Now someone in my house hold was sick too but I wasn't home all that often and with my immune system I rarely ever get sick. My symptoms are just sneezing (like a dripping nose) but that went away but im still coughing like all the time. Is it possible I have HIV or am i mostly likely just suffering from a cold or viral cough. I would go get tested but I dont have insurance and cant afford anything. I feel like im just being paranoid and I hope so.