The stereotypical "nice guy" is a term for someone who thinks they're a nice guy, but then turns into an asshole when they don't get what they want. Not related.

Or even more specifically: it’s a person who has an ulterior motive for being nice instead of being altruistic for its own sake.

Yes you would. Exactly why when you do not feel good about yourself, dragging yourself into helping others is just going to make you feel awkward, fake and used. Someone who is not feeling good about who they are should probably focus their energy inward for a while.

I've always been happiest when I have regular volunteer work that I'm doing. I've volunteered in homeless shelters, as a crisis counselor, and doing wildlife rehab. The work is never glamorous, but gets me out of my head and using my hands again. On the best days, I can see that what I'm doing has a real, tangible impact on another living being, and that gives me really great joy. On the worst days, I'm still "in it" with a community of people who are dedicated to the same cause.

I've never felt awkward, fake, or used. I've only felt like it's given me community, purpose, and meaning in my life. Your mileage may vary, but volunteering has gotten me through some pretty dark times in my life.