I think a lift is very possible in your case, with or without a reduction. However, given how young you are, there are a couple of very important aspects of breast surgery that you need to be aware of:
First of all, if you are a smoker, you need to be off of all nicotine products (gum, patch, and of course cigarettes) for at least 1-2 months before surgery and 1-2 months after to give yourself the best chance at normal healing.
Once you have the procedure, it's important to realize that if you don't wear good support bras, over time, the droop of the breasts will come back-- this usually happens over several years, but I always tell my patients to continue to wear good support bras to maintain the results that they have invested so much into already.
While the chances are low, it is possible to lose some sensation to one or both nipples after a lift or reduction. This may or may not be important to you, and some women with heavy, ptotic (drooping) breasts have developed some loss of sensation already over time. Be prepared for this, and if you absolutely do not want to lose the sensation to the nipples, you may want to reconsider surgery. Again, the risk of this happening is low, but it exists.
There is also a chance of a decreased ability to breast feed after surgery as well. For many women, having the opportunity to breast feed once they have children is very important, and some women simply cannot breast feed, even if they have not had any breast surgery. But if any breast tissue needs to be removed as a result of the procedure, the risk exists that you may have less of a chance of breast feeding after the procedure. So if this is important to you, you may want to think it over as well.
There are many well-qualified surgeons in the Arlington/Dallas area, and they will be able to review their prices with you in detail, as there is great variety in the prices based on surgeon and region.
I wish you all the best of luck! Talk to one or two Board-Certified Plastic Surgeons before choosing the one you're most comfortable with,