Can I pursue a master's degree and research career after taking 16 years to finish undergraduate?
Extended periods on your CV are fine as long as you can explain why they are there. 

From my understanding, you took as long as you did because you did a full-time undergraduate degree in Mathematics followed by your Masters degree, while still doing TA duties on the side, and then also attempted to do the Psychology degree at the same time. This is a huge amount of work. You also stated that you had to pause the Psychology degree for a few years. Given that your full-time Mathematics path would have taken around 6 years (correct me if I am wrong) and the full-time Psychology undergrad would have taken 6 years, your situation makes sense. 

All you need to do is be able to explain the timeline - and you can! I would not worry too much about applying. You have demonstrated that you are completely capable of higher-level study by getting your Masters in Mathematics (which isn't at all easy)! 

Good luck! I really hope this works out for you!