Hi Ryle,
You're not the first to remark on something similar when first using an e-cig. Infact when I first got mine I had similar symptoms. These have now pretty much gone away thankfully.
What I think causes them is associated with the way we tend to use our e-cigs when we first get them, that's pretty much flat out use. That coupled with none of the bad products from tobacco smoke to cancel out or reduce the affects of the nicotine we inhale.
Lets consider those two things a little more.
Cigarettes have a natural finish point, we burm em and bin em. E-cigs don't have this cut off so we tend to continue using the thing for longer periods of time per session. This is of course going to increase our overall intake of nicotine. Good comparison you made to having way to much coffee. The remedy is in the hands of the user to self-regulate the amount of time spent sucking the thing.
One of the fantastic advantages of e-cigs is there are none of the bad things in the vapour mist that are present in cigarette smoke. In particular there is no CO (carbon monoxide) or CO2 (carbon dioxide) both of these gases have the effect of reducing the "hit" we get from the nicotine contained in tobacco smoke. If you like it can be said that we get effects of a far purer form of nicotine rather than the effects from a junk cocktail of things in tobacco smoke.
There are a couple of other minor side effects you may notice from e-cigs and both are associated with the PG (propylene gylcol) that is used to create the vapour. The first is some dryness and slight irritation of the mouth and throat. PG does tend to do this and it quickly passes as you become accustomed to using it. Increase the amount of water you drink (never a bad thing) and try sucking a hard sweet, I use tic tacs. The increased water intake will help the dry mouth and the sucking action soothes the throat irritation.
The second is some tiredness or heaviness in your limbs. This is related to what happens to PG in your body, PG is metabolized very quickly into lactic acid and is then excreated rapidly from your system. Lactic acid is also produced by muscle tissue when you exercise, that's what gives you the burn feeling, most people will have experienced a "stitch" at some point, this is an excess build up of lactic acid in the muscles.
Neither of these two are a significant issue and do go away quite quickly.
One last thing ... Some people are more sensitive to PG than others, if you have anything more than some minor niggles using PG or the niggles get worse either consider stopping completely or switching to a VG (vegetable gylerin) based juice.
I hope that helps
