Only 1 percent of parents said they were concerned over safety for those two vaccines. Side effects for the HPV vaccines include pain and redness or swelling at the injection site. In addition, other mild reactions can include dizziness, nausea and headache, the CDC reported.Fainting is also a side effect, but it is important to note that it can occur because of any vaccine or injection.nly 1 percent of parents said they were concerned over safety for those two vaccines. Side effects for the HPV vaccines include pain and redness or swelling at the injection site. In addition, other mild reactions can include dizziness, nausea and headache, the CDC reported.