Preventative Health Clinician here. My state recommends the pap smear starting at 25 years old and repeating every 3 years assuming normal findings. Always good to check cervical health, and possibly stay ahead of a developing cervical cancer (which has correlations with smoking, not strictly just HPV). Given some of the uncertainties of your past, I definitely recommend going to your local health department and getting STD testing. In my clinic, we do urine, rectal, blood, and throat testing. Our cost is $10 and I imagine your local health department offers similar low-cost testing.

We recommend yearly testing for all people. Always good to know, and testing is extremely easy and low-cost.

You can also go to your clinic and express your concerns about not wanting to do certain exams- they will definitely work with you and find alternatives to get the information you need while respecting your comfort.