Yes, depression can be a symptom of peri-menopause, so is lethargy, apathy, hot flashes, brain fog, weight gain, weight loss and a host of other things.
Before your doctor put you on Loestrin did he take blood test to determine what your serum blood levels were for estradiol, progesterone, testosterone? He may not have as some doctors don't in the beginning due to the flucations but it's a great reference point for the future. To feel good we need to have balanced hormones and the Loestrin could have more of the P or E than you need and is keeping you off balance. Have you been on them long enough to even our if it were the right dose? If it were me, I'd have him test my hormones while taking them to see if the ratio for E to P is good.
That said, I was able to stop the hot flashes with one soy burger a day in the beginning and cutting out all sugar and wine. I'm now post and do take BHRT. It's still a daily struggle to get things balanced and I will still get hot flashes if I have sugar or alcohol. The statement ..growing old isn't for sissies.. is so true. And it happens so quickly. I use to think menopause only happened to old people.