It Is Possible. When the immune system is challenged by an infection, and you have severe pain, it is possible to feel weak. Specially if you are diabetic, have hypertension, or are immuno-suppressed due to illness, or medications. Why not visit your dentist and find out what is wrong so that you can have that treated, and see if there is a change in your status. If not, you may need to visit your primary care.
Possibly, but... While it is tempting to link your tooth-related problem of swelling and pain with general body weakness, doing so without a complete exam by a doctor may lead you down the wrong road. Infections anywhere in the body can affect the immune system, which is linked to how you feel. Many tooth infections, however, exist without any perceived effect on energy levels. See a dds and md for evaluation.
EMERGENCY! Swelling means the infection is spreading, and this can produce an airway problem. The spreading infection can affect your entire body. You must see a dentist now. Don't wait. This will not get better by itself, only worse.
Probably. It certainly can be the cause. Get to the dentist asap. Cold packs to keep swelling down, . Ibuprofen if you can take it. The dentist will probably give you antibiotics and of course treat the tooth.