First we will have to check if it is dental or a skeletal issue which has caused the tooth to protrude so much that you can't close your mouth.
If it is a dental issue then it can be treated by braces, but if it is a skeletal issue then the treatment is a combination of orthognathic surgery and braces.
please visit an orthodontist with an OPG and Lateral Cephalogram (x-rays). this will help in quicker treatment and avoid multiple visits
As per your description of not being able to close your lips because of proclined teeth, the best treatment option for you will be braces treatment only and that will require a duration of 1 to 1.5 years....
please visit the dentist for a proper clinical examination so that the best treatment options in your case can be advised to you....
Yes it is possible by orthognathic surgery within no time. We can move the bone with the teeth inside as much as your face requires. We need to get some measurements done for that purpose. On the basis of your complaint and the experience I have in orthognathic I feel your problem will get solved by anterior subapical osteotomy. Let us know when you travel to Ahmedabad. Visit us at Face maxillofacial and dental hospital,ambawadi.
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Get an opinion and have a look at some patients photographs treated by us.
It is vert difficult to answer this situation without seeing mal alignment of your teeth. But according to the situation you have mentioned you need orthodontic treatment that includes braces that is the best way to deal this deformity and it may take 1-2 years to complete treatment, again difficult to answer without seeing patient. Other options may include removing those inclined teeth and giving fixed, perfectly aligned prosthesis if there are severe time related crises but I dont generally prefer. Yet get check up done by the dentist, he/she may answer, only after getting your check up done.