If you have been using the Suave you have been cleansing, there is nothing gross about conditioner only washing, done well it is effective at removing sebum, skin cells, heavy oilings, many water soluble products.
Silicones are -cone, -conol and -xane not -one. If this is the correct ingredients list that product is packed with silicones unfortunately, can you return it to your stylist and teach her how to recognise silicones?
"Cyclopentasiloxane, Cyclomethicone, Dimethicone, Carrot Oleoresin, Argan Oil, Babassu Seed Oil, Linseed Extract/Aloe Barbadensis Leaf Extract, Flax Seed Oil, Coconut Oil, Retinyl Palmitate (Vitamin A), Ascorbic Acid (Vitamin C), Tocopheryl Acetate (Vitamin E), Ceramide 3, Hydrolyzed Amaranth Protein, Hydrolyzed Soy Protein, Hydrolyzed Vegetable Protein, Laurydimonium Hydroxypropyl Hydrolyzed Soy Protein, Fragrance."
Silicones impart faux slip and shine, all they do is make the hair feel and look awesome, they do not nourish the hair at all but may block out beneficial ingredients. It's not so much that they are 'bad' but more that they are not 'good' for the hydration or health of hair (unless you are flat ironing). You need to use a sulphate or cocoamidopropyl betaine shampoo to remove them not vinegar.
If your hair is damaged or porous maybe try deep treatments such as coconut oil and honey, over time these will make your hair look at feel awesome, be healthier and more hydrated. HTH.
2a-2c, medium texture, porous/ colour treated. Three years CG, growing out mechanical and chemical damage = breakage and very high porosity. Past armpit length heading for waist.
CO-wash: Inecto coconut
Treatments: Komaza Matani, coconut oil, Hairveda Sitrinillah
Leave in: Fructis Sleek & Shine (old), Gliss ultimate volume, Inecto argan
Styler: Umberto Giannini jelly, Boots Essentials gel
Experimenting with: going back to basics