My nose has a very straight bridge and is quite fat at the end. Could I get a button nose with surgery? (Photo)

Thank you for your question and the attached photographs.
Assessment for residual problems related to Bell's palsy would be important before advancing to surgery. As a general statement, most people do not have nostrils that are at the same level, but the differences can be sometimes more subtle and sometimes more visible. Bringing the nostril height to better symmetry is possible but perfect symmetry is not typically achieved by surgery.
The nasal tip skin appears moderately thick, so if you would like to achieve a "button nose" through surgery maintaining the to projection relatively close to the original would be important. It retains more tension in the skin and allows more definition from the front view.
To define your goals more accurately computer imaging and simulation would help and would give you more guidance whether surgery is likely to provide a result compatible with your aspirations. It would also help to understand whether a "button nose" would integrate with your facial features and whether you would like the overall balance.

The main problem is that the tip of your nose sticks too far out from the face. You need the bridge lowered so the tip is placed closer to your face as well as a tip plasty. If you only work on the tip I don’t think the result will be right.

After seen your pics; We think a complete open rhinoplasty should be best option for you. Your tip, nasal bones and dorsum  need some work
Best Wishes