If you have a perfectly good tooth buried in the bone then you should really consider doing what the dentist recommended. It will be a short term inconvenience to go through the surgery and possibly orthodontics to bring the tooth into line with all your other teeth. A crown would have to anchor off some adjacent teeth and this presents many long term problems.
Healing is well under way in most cases by one week however the wound will be immature for several weeks and hence you need to protect the site from being traumatized and generally keep the site clean for the duration. A crucial aspect also is to make sure the rest of the mouth is kept clean, this keeps the bacterial load low elsewhere and further enhances healing.
There are a number of factors to consider. Firstly your teeth look to be about the right dimension with just is a little crowding present. Making the correct diagnosis is key. A helpful photo is the "lips at rest", ie your lips just gently parted, this lets us know the if the teeth are generally well positioned in the face. If approximately 2 mm of the teeth show at rest then you could have a hyperactive upper lip, this being the case there are a number of treatment options for example botox which would be a simple but temporary fix. If a considerable amount of your teeth are exposed with your lips at rest then the height of you upper jaw could be larger than normal and jaw surgery could be required. There are many treatment options that you will need to fully understand and could involve referral to a number of dental specialists.
It is really important to accurately diagnose the factors that currently influence your smile as this will dictate treatment outcomes to a great extent. What I am getting at is I think your lips may lift unevenly, rising higher on the right to give an uneven gummy smile. Get a comprehensive evaluation from your dentist and ask them for a simulation of the end result. There are ways to address an uneven lip and your dentist can discuss this as part of a comprehensive evaluation.
What you describe is also called a crown lengthening procedure. Definitely let your surgeon know that you are quite anxious about receiving treatment. They can take steps to help you feel less anxious prior to surgery and also ensure there is minimal if any discomfort before, during and after the procedure.