Your open bite can and should be corrected. I feel confident that it could be corrected non surgically . However, you probably need speech therapy for the tongue thrust. Otherwise, your tongue habit could open your bite up again.
Correcting open bite with DNA Appliance (Epigenetic Orthodontics)
Most cases with open bites are primarily Orthopedic rather than dental only. A DNA appliance will allow you to orthopedically grow bone and Pneumopediclly grow airway. Tongue thrust is usually an airway issue and often relapses if airway is not corrected.
#Cross-bite corrected without surgery
Without photos, it's hard to be exact, but it is likely that your cross bite can be corrected without surgery. You may need an appliance that limits your tongue, which could ultimately affect your speech, but a non-surgical resolution is possible. Depending on the dentist you choose, he or she may or may not be able to correct your bottom teeth using Invisalign. However, at 16 years old, you would be a good candidate for metal braces (even though, you may wish you were not). Good luck to you and I hope this helps. "Follow" me on Real Self to ask more questions of me.
Sarah Thompson, DMD
O'Fallon, IL and St. Louis, MO