I just found out that to work in my chosen profession, I need at least a BSW, not a BA in Psych. Now what?

Definitely go straight for the MSW. The second bachelor's is going to take a lot more time and money, which you might as well spend getting the MSW. The MSW will also allow you to get other social work jobs down the line if you find that you want to work in a different field within social work. Plus getting your master's is better than just doing the minimum.