What procedure could help my arms after having liposuction that left the skin on my arms very loose and dimpled? (Photos)

Difficult problem but it can be helped, maybe not completely cured. There are several non-invasive treatment protocols that can be used alone or together. 
Lipomassage can help cellulite (not only in your arms, but in the thighs.). this uses an external device that rolls and suctions the skin without an incision. I recommend 6-12 treatments depending on the severity of the problem and also the quality of the skin itself. It will smooth and release the dimples and decrease edema. 
Thermage is a device to tighten the skin by use of radiofrequency rays. This can be done after the lipomassage series and can repeated every 4-6 months. 
Skin care is very important on a daily basis. The skin must be kept moist and lubricated or else it will look even more dimpled. Also, avoid too much sun exposure that will also dry out the skin. Daily use of products like Medical Barrier Cream (Epionce) will lubricate the skin and make it look healthier! 

Thank you for your question about addressing the excess hanging skin on your arms following arm liposuction, and for providing your history and pictures. The solution to your concern is an arm lift, also known as arm reduction or brachioplasty. Since you're dealing with excess skin, removing this skin is the primary goal of the procedure.
The most suitable type of arm lift for your situation appears to be one that involves an incision extending from the armpit to the elbow. This approach effectively addresses the excess skin in the upper arm area. The placement of the scar, between the biceps and triceps muscles, is strategic so that when your arm is at your side, the scar remains relatively hidden.
The brachioplasty is typically performed under general anesthesia and the procedure can take around three hours to complete. You should anticipate a recovery period of about two weeks. During this time, it's important to follow your surgeon's post-operative care instructions to ensure the best healing and aesthetic outcome.
I hope this provides a clear answer to your question about managing the excess skin following arm liposuction. Wishing you the best of luck with your procedure and recovery.
Sincerely,
Dr. Katzen

The areas where you have dimpling could be secondarily filled with fat or even Sculptra but loose skin will only be effectively dealt with by excision as in an arm lift or brachioplasty  That should give you the best improvement of the skin laxity and dimpling.