I take both iron pills and am on the birth
Hello, I'm Dr. Branch, thanks for using Ask a Doctor. I have never heard of birth control, patch or otherwise, interfering or interacting with iron supplements, and could not find anything when researching this. Especially since the birth control patch avoids intestinal involvement, I don't see any way that it would interact with the iron you are taking. So I would be reassured that it is safe.
You are unlikely to overdose on iron as long as you are monitoring your ferritin periodically.
One other thing, recently studies have shown that using iron every other day resulted in better absorption and less side effects than every day. If you are not already taking the iron every other day, you could bring that up with your doctor to see what they think.
I hope that helps, please let me know if you have any other questions about that and I would be glad to discuss it further with you.