I want veneers/crowns to close tooth gaps, but I have an underbite and a crossbite. Will it make this issue worse? (Photo)

Looking at your [pictures, you need to see orthodontist first, have a consult, estimate of the time it takes to fix your bite, I do believe that you will be needing also an orthognathic surgery in conjunction with orthodontics. That is your best option.Now for cosmetic purposes if you still do not like the shape, the color and the gaps in your teeth, after going ahead with braces, you need to see a cosmetic and reconstructive dentist.If you choose to refuse orthodontic treatment, you can also have a consult with cosmetic dentist to see what can be done for you, although this is a compromised solution in which many patients choose to get done. You will be needing a complete evaluation by a cosmetic dentist, including radiographs, impressions, bite analysis,and go from there. The cost of your dental treatment will not be cheap either way you choose to go with. A definite complete dental evaluation by a top cosmetic dentist is your best bet.

Without question, your best treatment option is to find a very experienced orthodontist.  Your case is very severe and it may require braces and surgery depending on the amount of improvement to your smile you would like to have.  I do not think that porcelain veneers are a good option for you.  I am not saying it can't be done, just that it is not your best option . Good luck.  

Adressing your bite should be your priority.Seek am orthodontist who
performs hundreds of these procedures who is an
expert in this field.Best of luck,James Asaf, DDS