Can an implant and its crown be safely removed, without further work required?

I have recently had an implant done on a tooth that has been a problem for 2 years. The implant has not solved the problem and the tooth still throbs almost constantly. It started 2 years ago when, while eating a caramel, I loosened a crown. This crown had never caused me any problems at all. The tooth in question is my bottom molar, second from the back. I went to the dentist, who took the crown off and re-attached it. Since then, it has been nothing but painful. It is a pressure-like pain; I remember telling the dentist that it felt like there was too much cement in there. The crown was removed and replaced twice; then I had a root canal and a whole new crown done. Still no relief. Finally, I had the tooth out, which did bring relief. This has all been over the past 2 years. Several x-rays have been taken, which all show nothing wrong. The dentist offered me a discounted rate on an implant, so I thought I’d try that. The implant itself was not too painful, but once the crown was fitted on top, again, I have the pain, which feels like extreme pressure and throbbing, sometimes radiating to my ear. X-rays show nothing and the dentist says it looks good. The implant crown was fitted about 3-4 weeks ago, and the pain is getting worse. In the past week or so the molar directly above this tooth has started to be sore, with throbbing pain radiating back to my ear. These two teeth do a relay act, one throbbing for 10 minutes, then the other. I am going to have the top tooth checked out; it is an old crown which may coincidentally have developed a problem. Otherwise, I feel like I have some sort of overactive nerve situation. In desperation, I am seeing an acupuncturist to help with the pain. I’m tempted to have the implant removed, or at least the crown taken off. I am more than willing to live with a gap at this point! Can the crown be removed, and possibly the implant? If the implant is removed, will the hole just heal? I can’t really afford and am not interested in anymore invasive work done on this area. Any comments or suggestions gratefully accepted.