This actually happened to me. The doctor said the birth control was raising my blood pressure. I said "I don't think so" but turns out she was right. So I quit them and immediately got pregnant.

But when you say "occasional headaches"? The other thing I found out when I quit them is that they were amplifying my migraines quite a lot. Occasional headaches does not adequately describe that pain, vomiting from the pain.

(ETA - the copper IUD was also a nightmare for me, but eventually landed on the hormonal IUD and that was fantastic, those got me through to menopause - Birth Control doesn't have to be the pills, and not all of the 'hormonal' methods are the same. And an IUD will last longer than the current administration)