Uh... Penicillin can sometimes give people GI issues, primarily diarrhea. Most people have minimal side effects. Other than that it's not going to affect your training at all.

Edit: extraction should be NBD unless you're a bleeder. Keep it clean for a few days and it'll heal up just fine. The implant is a little more invasive, it's a multi step process, with the first step being the hardest physically. They'll cut out a section of bone, place in the implant "socket" if you will, and let that heal into the bone. They they have to install the actual tooth. It's... Not the most pleasant process, but I sincerely doubt it'll impact your training significantly, save for a day or two following the first step of the implant.

given that you've just had an extraction, I'd gather that staying out of the water for the first few days is a given and there'd be no harm in just dialing the training back a couple of notches, maybe give the track sprints away for this week and replace it with a tempo run.

I had an implant earlier this year and it was close to 2 weeks before I could run at high heart rate. Anything over 140 created a lot of pressure.