Freaked out brushing and flossing my teeth tore my lip augmentation stitches? (Photos)

Only an exam in person would clarify whether or not you have a problem. You are best to see your surgeon for an evaluation in person.

Good Day. 
I understand your concerns, however, you are most likely safe. Seeing your surgeon to ensure the implant is not exposed is strongly recommended. 
The photograph does not reveal implant exposure. If there is some exposure, you will most likely not have implant extrusion or infection by cleaning the wound, placing one suture and continuing oral antibiotics. The best antibiotic is Cleocin (clindamyacin) since it covers oral bacterial flora.
Since the lip has a huge blood supply, the lips heal rapidly and the rich blood supply minimizes the risk of infection.
If an infection develops despite oral antibiotics, I would recommend removing the implant, waiting 4-6 weeks and then reinsert. The advantages of soft silastic is easy in, easy out and easy in again, if need be. 
I have completed 140 silastic lip implants and have not seen any patient suffer an infection. A few had the absorbable suture fall out prior to the expected 7-12 days with no complication.
Iin summary, see your surgeon. He will examine you and determine if wound suturing, oral antibiotics or other treatment options required. I think you will have no problems. I hope this minimizes your anxiety.