I don't have any piercings, but I frequently have an infection inside my bellybotton. When I go to clean it out I can feel some discomfort all the way down my groin. Could it be a symptom of something else (prostrate, etc.)?

You need to have this checked out. This does not sound like an infection to me, but rather a hernia. Hernia's can be repaired, but you need medical attention for this. Please make an appointment with your doctor. A hernia can be a serious conditon.

If I jam a Q-tip or other object in my navel, I have discomfort too - I believe most people do. It's a sensitive area.

Are you overweight or is your navel deep? If so, you may be suffering from intertrigo - an inflammation of the skin caused and worsened by sweat / moisture, poor air circulation, friction, etc. When it involves the navel, it is called "navelitis" (no kidding! ). It could also be aggravated by your picking at it or by whatever substance you are using to "treat" it. Neosporin and other such over-the-counter remedies can actually worsen this condition in some people. The treatment often includes keeping the area clean, dry and ventilated. In some cases a medication may be prescribed. If you are overweight, you need to lose weight. There are other conditions (some quite serious) that may mimic this - so, as J 9 recommended, you'll need to see a doctor (dermatologist, if possible).