Yes, they can be hereditary. They can also be brought on by weight, menopause, and/or thyroid issues.
I only discovered that because I didn't know that I had varicose veins until I saw a doctor for swelling in my legs, ankles and feet a couple of years ago. Mine is not hereditary. On top of discovering the varicose veins, I have DVT (deep vein thrombosis) in one leg that needs to be monitored. I've had surgeries for the varicose veins and things are much better now.
Please go see a vein specialist. If yours is puffy and bulging, it very well may be more than just a spider vein. Good luck