is it ok to be on the rod AND take the pill at the same time?

I have had the rod for 3 years and just got my second one put in 2 months ago, my periods have always been irregular so when I got on the rod it was a nightmare. I had my periods allll the time for so long. But it wasn't so much full heavy the whole time, It would stop for a day or two and then they would come back and i would be spotting brown stuff for ages 😖 then after a year or so it slightly got better so that's why I stayed on it. My point of view was having my periods is better than getting pregnant (so young)
Now, I get my periods for about 1 and a half - 2 weeks and some times maybe even for abit longer.. the reason I chose to stay on the rod for so long and decided to get it in the second time was because I liked the idea that it was already in my arm doing what it had to do and I didn't have to remember to take or do anything (plus the fact that you only have to spend $10-20 for the rod and that lasts you for 3 years) 
But now I'm honestly over having my periods for so long so I went to the doctor and spoke to him about possibly getting the rod taken out and going back on the pill. The doctor suggested staying on the rod and going on the pill for 2 months and that will regulate my periods and get them in a routine of only coming for a week once a month. Which all makes sense but idk how I feel about being on 2 contraceptives with twice as strong hormones all going through my body 😕 surely that would send it out of whack and have strong side effects?