Lately, i have started getting headaches shortly after my top teeth hurt and, if running, they almost feel loose. i just got over a head cold. could they be related?

Maybe: They maybe related. It is very difficult to diagnose without an examination. You need to see a dentist asap.

Could be related: If you had sinus infection very common for upper molars to hury but should get evaluated by your dentist.

Could be: If multiple teeth hurt it could all be caused by sinusitis. If it's a particular tooth, you may have a dental issue. Only an exam will really tell the story.