I haven't seen Sunsilk around me in a good while, but last time I looked, their ingredients were far from CG - just the shampoo contained both sulfates and silicones. Maybe just look for basic products - shampoo and conditioner - with hair-friendlier ingredients.
Looked on line and couldn't find anywhere that actually listed their ingredients, even Unilever's own site. I did find one other than theirs that discussed
them somewhat, and it specificially mentioned both sulfates and silicones, so doesn't look like they've changed that.
Fine hair can almost always use regular doses of protein - it sounds like that may be actually be what you mean rather than thin, though they often go hand in hand. Protein will make it stronger and less prone to breakage. I love Spiral Solutions repairing protein treatment, available here in Curlmart, but you can also find plenty of others or make your own. You can find help with that here.