Thank you for your question. Unfortunately the only way to straighten out your teeth without braces is to have veneers placed on your teeth. There are options other than fixed braces to align your teeth such as invisalign, which is a removable plastic brace that fits over your teeth, these need to be changed every few weeks until the teeth are straight. It would be worth going to see an orthodontist for an opinion.
Usually when a dentist hasn’t had much experience in placing veneers they are reluctant to shave teeth down. It is true that having veneers done is destructive to your teeth and is an irreversile procedure. Therefore you need to speak to someone that knows what they are doing before you take the decision to have them. Veneers can be placed on teeth after very minimal preparation and if they are prepared by a dentist with experience and made by a laboratory that knows the correct techniques and characteristics of teeth (there are many labs that don’t) then your teeth will not only look good but the restorations will be long lasting and life like.

It is your decision at the end of the day. If you decide to have veneers then please find someone that knows what they are doing. Ask to see a portfolio and ask the dentist about the laboratory that is used. Most good labs have their own website. This way you can make an informed decision.

Kind Regards