Problems with dental implants. The bottom ones move, and cause pain. Can I have them fixed?

Unfortunately pain and mobility on implants is not a good sign. mobile implants are failed implants. Have them evaluated by your dentist/ surgeon to make sure they are mobile. (Sometimes the screws which are attached to implants are mobile).  If infact the implants are loose, they should be removed before causing further bone loss and infection. 

If you have recently taken the procedure of dental implants, then you should be well-known to the problem associated with it.
1. Risk of infection-It is quite common that you might undergo dental surgry for better results, but it increases the chances of negative response.
2. Fracture-If you grind your teeth, then it might force ongoing implant can cause fracture. 3. Nerve damage-Nerve damage causes different types of dental issues and sometimes, the dental implant needs to be placed again.

I would see your restorative dentist as soon as possible.  A loose implant can be either the connection between the crown and implant is loose and the crown is pinching your gums or the actual implant may be loose and needs to be removed and redone.