If you have been to your genetics service in the past, you should contact them directly for advice. If not, you should visit your GP again and request a referral to your local genetics centre for an assessment. A list of genetics centres can be found here and most do outreach clinics in local hospitals.
Prior to your GP appointment try and get as much information about your family history of both ovarian cancer and breast cancer (in both your parents’ families).
Based on the information you have already provided you may fall into a risk group who should be offered genetic counselling and testing. The fact neither your mother's or grandmother's cancers were ever tested for BRCA1 or BRCA2 gene mutations can make the genetic testing a bit more complicated but it is still possible to do this by testing you and/or other close relatives. However, it would be crucial to get confirmation of the diagnoses in your family by getting the hospital pathology reports or the death certificates.
Currently there is no evidence that screening programmes for ovarian cancer in the general population or in women at high risk of developing ovarian cancer offer any benefit. If it turns out that you may be at high risk for ovarian cancer because of your family history, then the genetics team would discuss how best to manage your risk.