It is very difficult to let you know whether or not an implant would be suitable for you. The answer depends on a number of factors;

If the mobility is due to gum disease. This causes infection and bone loss from around the tooth. Implants need to be placed in infection free environments. If bone has been lost there may not be enough to place the implant in. A bone graft may be needed.

If the tooth is in the top jaw near a sinus, there may not be enough depth of bone to place the implant into. A CT scan and bone graft may be needed.

If the cause of the mobility and fracture of the other tooth are due to forces incurred during biting and chewing, this may need to be corrected before an implant is placed.

There are certain other considerations; implants have a much higher failure rate when placed in people that smoke.
If you immune system is slightly weaker than normal, ie diabetes, there is a higher failure rate.

In either of these circumstances the dentist placing the implant may not guarentee it for a period of time after placement.
Before any dentist carries out treatment, full records of your mouth should be taken, this would include, x-rays, photos, casts of your teeth, gum survey. this will allow a thorough diagnosis and treatment plan to be formulated for you.

I hope this helps
Kind Regards