Do I have a abcess or spider bite?

Depends. Most spider bites are like other insect bites and may hurt at first but afterward, like with any break in the skin, infection needs to be watched for. Spiders get blamed for a lot of insect bites but many are not spider bites. Generally, if the site is red, swollen, warm and painful, see a physician to determine if an infection is present and treatment is needed.