My aunt tested positive for covid 2 weeks ago. she still has lingering cough, is it safe to see her or is she still contagious?

Hard to say for certain but she is probably ok to be around for now. Recommendations have changed and continue to change, but the general consensus is that people are probably not contagious after 10 days if they had mild to moderate disease or 20 days with severe disease. Cough after a viral illness can persist for a long time, as long as 2 months, long after the infection is gone.

If you are fully vaccinated, there is little risk in seeing her now. Both of you should wear masks. If you are not vaccinated, get vaccinated. Your aunt also should get vaccinated/boosted.