How Long Should I Wait to Get Dental Implants After Extraction?

Sometimes they can be done all at once, but if not then there is a waiting/healing period.  A general rule of thumb is 6 months, but in some cases you can start in 3-4 months.  It really depends on the area of the mouth and type of bone graft used.

it depends on the case to case, some time the grafting is usually done in 2 -3 weeks along with the placement of the implants and some time it is delayed due to multiple reasons and done after 3-4 months, some time is done together some times its staged

How long after an extraction should you wait to place a dental implant?
Assuming that you had a bone graft done at the time of the extraction, then it will depend on the condition of the socket at the time of the extraction.
If there was no significant bone loss, then the implant can be placed 12-14 weeks later.
If there was significant damage either before or during the extraction, then it may require significantly more time to heal before implant placement. 
Hope you found this info to be helpful,
Dr Champagne

This really depends on the particular case specifics in terms of the  presence of infection , amount of grafting required , cosmetic requirements and  even sometimes the medical history of the patient..

In some instances an implant can be placed at the time of extraction with grafting , sometimes  wait 3-6 weeks following extraction  and sometimes if it is a more extensive bone graft it could be 6 months. 

The best alternative will be to get the teeth extracted and place the implants at the same time so you don't go through surgery twice, but as you have an infection and you need a bone graft, the best way to proceed in your case is to wait at least 6 months before placing implants as they risk infection too and you need the bone to get attached properly.