The proper answer to your question does require more information about your situation but heres what I can tell you.
An implant failing a few days after being placed is rare but could be due to infection left behind after taking out the original tooth and or not enough bone graft being placed…or not allowing enough time to let the bone graft integrate before placing the implant/screw.
If the space for the missing tooth was wide enough to house a dental implant/tooth, then the space may not close completely, leaving open contact/food trap.... but it is not impossible.
Successful treatment with braces involves your entire mouth/bite. Changing your bite by shifting teeth around (to close such a big space) can affect your neuroskeletal alignment. I would seek a consultation with Orthodontist (specialist) first before making this decision. Even if your general dentist recommended braces to close the gap, I would still seek the opinion of a specialist in this area of dentistry to make sure braces will be an ideal long term treatment option.
Another route to go is to bone graft the implant site again and allow more time for the bone to regenerate in the space before placing the screw or doing a bridge. The bridge will close the space with a crown that is connected to the adjacent teeth/crowns. There are downsides to a bridge but it will probably be the least invasive and less costly way to achieve the goal. I would also bone graft the site regardless of bridge or implant.
Bottomline ....see a orthodontist and periodontist....get second opinions.