This is a great question as this problem is becoming more and more common. The likely cause of your spider bite-like bumps is an infection caused by MRSA (methicillin-resistant staphylococcus aureus). You might have heard this strain of bacteria referred to as a "super bug" on the news. This is due to the fact that it is resistant to some commonly used antibiotics, which can make it more difficult to treat. The symptoms of MRSA depend on where the infection is, but most often it causes sores or boils on the skin as you have described. Although most cases are mild, MRSA can occasionally be life-threatening so it is important to seek care immediately if the infection is not responding to antibiotics. MRSA is spread by contact and is estimated to be carried by about 1% of the population. To prevent recurrence good hygiene is key. Wash your hands often and keep any openings in the skin such as cuts clean and covered until healed. Wash personal care items such as towels frequently and always use a clean razor when shaving. Only take prophylactic antibiotics under the guidance of a physician as frequent antibiotic use can lead to further resistance. Sometimes a large boil needs to be lanced and drained. I would recommend seeing an infectious disease specialist
who sometimes will recommend skin washes and intranasal sprays to attempt to eradicate the bacteria.