Best Option for Lines on Chest Caused by Sleeping on my Side?

Judging from your question, my guess is that your lines are probably from sun damage and loss of elasticity in your skin. "Needleing' of the skin would be an option to create some tightening, but I do not think that Botox, or fillers will give you what you are looking for.
Depending on the overall situation you may also benefit from a neck lift.

I assume you are discussing the actinic damage and solar elastosis of the decolette area. As mentioned by the other physicians, laser and/or IPL are options for this area. Prior to the devleopment of these advanced technologies the "low tech" use of serial low strength TCA peels were beneficial for improvement of this area.

Good Day Dimitra,
I have had some success in treating the "sleep lines" on the chest with Fraxel repair Lite treatments.  It may take a few, from 1 to 4 treatments, depending on how sound of a sleep you have been, but most patients are very happy with their results.
Pleasant dreams down under.
Dr. P

Usually lines on the chest are related to sundamage of years ago ruining your collagen and elastin. Sleeping on one side may create more lines there from compression. Newer lasers may help but there is always a slightly greater risk of scarring below the neck than on the face when resurfacing. Expecting only one treatment to provide maximal improvement would not be realisttic. The results are definitely not as great on the chest as they are on the face, typically. Botox may also help but will have to be repeated at least twice per year if not more.

Lines on the chest are somewhat more difficult to treat than facial lines.
We use Botox as well as resurfacing using the Fraxel Repair, also Sculptra as a biostimulator and occasionally Chemical peels to the the lines and sundamage on the chest.

When you look at your skin, compare the areas which are consistently covered by clothing to the areas that see the sun. It will become very apparent that the sun-exposed areas have a different texture, color, and more wrinkles. The chest area is no exception.
To improve lines on the chest, I believe that Fraxel Repair is the best technology to create improvement. Multiple treatments would be required to give the best results, 3-5.
Also, I would consider adding volume with a deep-tissue biostimulatory filler like Sculptra. The chest is not a common area to use Sculptra, but in the hands of an experienced injector your results would improve over laser alone.