Genital wart is shrinking by itself (no medication yet). is this a good sign that my immune system is acting on the virus or not necessarily?

Take HPV vaccine: Most women are able to eliminate HPV, the causative agent of warts. Taking HPV vaccine will protect you from other strains causing warts and cervical cancer. If you do not wish to be pregnant, use contraception all the time, every time. You may consider implanted contraceptive, or IUD. Practice safe sex. Get HPV vaccine.

Maybe: Although there is a good chance it will go away without treatment, there is no test to predict this. See your DR, preferably a GYN. Of course you should get HPV vaccine. It protects against 4 viruses associated with cancer of cervix, but not against 100 or so others. The vaccine does not alter existing hpv infection, only prevents future infection by a few specific viruses.