You call yourself a caffeine addict, getting the shakes from a fountain coke, ISAslot? My body only notices that amount of caffeine when I've gone a few hours without any Dew or Coke, and it only notices it then because I've started withdrawal.
If you rarely take in caffeine, then it can be a jolt to the system, and you may come down from the "high" and get shaky hands for awhile, or feel nervous (oddly, the effects of caffeine and many other drugs are the same DURING the effects as well as the comedown).
A 20oz Dew isn't really an insignificant amount of caffeine. A 20oz bottle of Dew has about as much caffeine as an 8 ounce cup of instant coffee; brewed coffee has another third past that in 8oz; so basically brewed coffee has 3.5 times as much caffeine as Dew, per ounce; a tablet of No-Doz or Vivarin has 200mg, a bit over twice the 92mg in 20oz of Dew. You're not supposed to take more than one Vivarin every 3 to 4 hours. With an intolerance to caffeine, it'll probably take longer to come down from it than some other people, even though you only had one drink.
In short: yes it's normal, it's an expected side-effect of caffeine, in someone who doesn't have a tolerance built up.