What is the best treatment for the wrinkles under my eyes and the loose crepey skin on my neck? (Photo)

Wrinkles under the eyes can be treated with a variety of options. In some cases, the only solution is surgical intervention such as a lower eyelid lift. Laser skin resurfacing could help, but this depends on the patient. For laxity of the neck skin, there are MANY "non-invasive" options out there, but most patients end up spending a ton of money and wasting their time with these devices. In many cases, a neck lift is indicated to tighten the neck skin, and 44 is definitely not too young for this type of procedure. In some cases, a mini lift is all that is needed. Laser resurfacing on the neck can offer some degree of tightening, but this usually offers only very mild results in the neck.
Be sure to see an expert like a facial plastic surgeon to review all of the surgical and non-surgical options in detail.
All the best,

I tend to start with less invasive options for someone in your age category.  There is no single best treatment, but you can see benefit with a combination of injectibles (Botox or similar for neck bands and lateral lower lid wrinkles) and topical treatment such as radiofrequency for both the neck and periocular regions.  These should help and hopefully keep the surgical options farther out for you, as you are still early for those.  

Some people require surgery to get the best improvement.  Non invasive options for improvement to the neck include:
botox, dysport or xeomin and/or fillers to help platysmal bandsthermage radiofrequencyultherapy high intensity ultrasoundPDO nova threads or instalift for liftingsculptra injections for collagen productionbtl exilis ultra, venus legacy, and thermi250 for constant collagen stimulationJ plasma or thermiRF internal tighteningI recommend a combination of fillers, lasers and microneedling/prp to improve under the eyes. I recommend getting a formal evaluation with an expert. Best, Dr. Emer