I think I'm similar to you. Caffeine has always made me sleepy and my mom too. We live in the South, so we were always drinking sweet tea at dinner. And we always were getting really tired afterward.
When my mom was younger though, she was getting a little drowsy on a long car trip and stopped at a gas station to pick up some No-Doz (caffeine pills). At the time she had no idea that caffeine could make her tired. When she got out on the road she almost fell asleep at the wheel because it made her so tired. Ever since then, she experimented with non-caffeine drinks and discovered that she didn't get tired with those.
Long story short, I'm the same way. I can't ever drink any sort of caffeine without crashing as soon as it hits my bloodstream. The only caffeine I take is in Midol. I have no choice with that, since Midol is the only drug that works for me during that time. I wish there was some way to get Midol without the caffeine, since taking it makes me useless all day. Also I notice that when the concentrated caffeine in Midol hits my bloodstream it makes me tired, yes, but also jittery at the same time. It doesn't last too long, but for that time my hands shake and I feel jumpy but also exhausted like I haven't slept in three days. It's a really weird combination.
I've never had any MD formally diagnose me. For the longest time, when I was much younger, no one would take my mom seriously when she said that caffeine put her to sleep. No one thought it was possible. Now whenever I tell someone that caffeine has that effect on me, they assume that I'm ADD or ADHD, which is very wrong. I've never had any attention disorder, no trouble in school, etc. But apparently, many people who are ADD or ADHD have a similar condition to me. *shrug* I just wish I knew better what was going on with my weird body.