I have swelling and pain in my upper thigh. There is no redness or warmth. I have heart problems. Do I need to worry about a DVT I have heart problems, and currently take 325 mg of aspirin daily.

Yes. A little bit. Swelling has many causes, but a simple ultrasound can determine any dvt. Ask your pcp to see you and guide you.
While . While many things can cause swelling and pain, you might have a case of dvt. While the use of Aspirin daily can decrease the risks of clotting, they might not necessarily eliminate it. I would contact you primary doctor and see if you can get non-invasive ultrasound testing to see if there is dvt. Even a blood test called d-dimer can help rule out clotting problems. If the d-dimer test is normal then you don't need the ultrasound. If it is positive you would need further workup.