Can wellbutrin (bupropion) make you shake like you have too much energy?

Yes. Wellbutrin (bupropion) is a mildly activating or stimulating antidepressant. Although most patients have no side-effects, some report a caffeine-like agitation or tremulousness. Tell you prescribing doctor, who may want to adjust the dosage or try a different medication instead.
Shakes. Yes, it's a side effect. It can be helped with certain additional meds, or by backing down on dose , then more slowly to titrating up. This should go away as you acclimate. If not, another med should be considered.
Yes. It is a stimulating noradrenergic/serotonergic anti-depressant that can cause tremor.

Related Questions

For what reasons might wellbutrin (bupropion) seem to make my hands shake and my veins in my hands stick out?

Wellbutrin (bupropion) Wellbutrin (bupropion) is a more activating antidepressant than some others -- in some people, it can lead to shaky hands, etc. Please speak with your doctor about your concerns; adjustments or changes may be possible. Read more...
Caffeiene? Regarding shaking hands- how much caffeine do you drink? I don't start patients who have high caffeine intake on wellbutrin (bupropion) until they have tapered down. It is an awesome medication except when mixed with caffeine. Read more...