It is easy to find 'OMG this happened around the same time / some months later so it MUST be linked' stories, but the HPV vaccine is extremely safe.
If you're going to have a jab with anything, there may be some side-effects (soreness where the injection was, for example) but chance of getting a serious ones for this is about 3 in 100,000 women getting the jab... and the chance of getting cervical cancer if you don't have the vaccination is about three times higher than that every year.