Can I achieve a slightly upturned nose like these photos of Amber Heard? (Photos)

In general, measuring the angles under the nose in surgery is challenging and rather imprecise. You have a starting advantage because the nasolabial angle is open and the changes on profile are mostly related to reduction in projection of the bridge, increased projection at the radix and slightly higher position of the tip defining points.
From the front view, reshaping the tip cartilages could create highlights closer to what you see in the reference photographs that you have provided.

You have to be mindful of the fact that it is never possible to generate a shape of the nose identical to someone else's, but a lot of the features that you like can be created for you.

The degree of reduction in projection for the nasal tip would need to be kept modest in order to make sure that the definition from the front is adequate.

Your nose is very strong in its forward projection from your face. The tip can be brought back closer to your face. We call that "de-projecting" the tip. 
The woman in the short video that I posted with this answer had the tip of her nose de-projected a significant amount.The bump can be taken down from the bridge, and giving the bridge a teeny-tiny concavity can help it look like the nose has an upturn. 
How *much* to elevate the tip, or lower the bridge, or deproject the nose? We figure that out with morphs, well before surgery. I'd love for you to see some excellent professionally-designed morphs of what could possibly be done with your nose. Morphs could also help you identify what's bothering you, and help you set a goal for the rhinoplasty that's accurate for your tastes. Profile and three-quarter views would be particularly important in morphing your nose. (Side note: in my opinion, morphs should always be done by the surgeon, or he should direct an assistant as she makes the morphs. Morphs should be made with a constant eye to what actually *can* be done in surgery, for that particular nose, and only the surgeon has that information and judgment. Another aside: I also recommend that you not show morphs made by one surgeon to a different surgeon. If a surgeon makes his *own* morphs, you get to see whether he understands the important issues of your nose, and how your nose should be changed. But if you show the surgeon someone else's morphs, and he says "Of course I can make your nose look like that," then you don't really know if he fully understands, or even recognizes, the important changes shown in those morphs. And you don't know if he can make those changes during surgery.)
Remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes that your nose needs require advanced techniques, and skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. And it also discusses how to take photos that are best for online evaluations.
Your nose is also a perfect example of why computer imaging by the operating surgeon is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?

Hello
Thank you for taking the time to share your question and photos.
The best option for you is to find a surgeon that is board certified in both facial plastic surgery and otolaryngology in order to properly address your aesthetic and possibly functional needs. The upturn in the nose you are looking for can potentially be addressed with a closed scarless rhinoplasty. In the hands of a properly experienced surgeon, this technique is beneficial because of the avoidance of a scar on the outside of the nose, much more rapid and comfortable recovery compared to an ‘open’ rhinoplasty, and less disruption of the nasal tissues. Additionally, if you have nasal breathing issues, you may be able to use your health insurance to offset a significant portion of the cost. 
Good luck!
Behrad Brad Aynehchi, MD