I'm a little confused by your 2 statements. The subject says 2 periods / month for 3 months (equals 6 periods), but your text says you've had A period every 2 months for 3 months (equals ?? one? two?)
All I can suggest is that you give it time. There are sooooo many horror stories about Depo and how it totally messes up your cycle that whatever your situation, it sounds 'normal' for a post-Depo user
As for the chlamydia test, unless you both have been tested for it before, there is no reason why not to have it, since either of you could have had it for ages w/o knowing.