Not all things natural are good, and not all things "chemical" or manufactured are bad. Though I don't necessarily recommend Neutrogena, there are general guidelines to commercial products that can keep you as safe as possible:
-avoid fragrance
-avoid drying alcohols (check out this
cheat sheet by an esthetician)
-avoid sodium lauryl sulfate (sodium laureth sulfate is milder and can be used as tolerated, but avoid it if you want)
-MAYBE avoid parabens and silicones (the jury is out on these, pretty much any research you can find is funded by either anti-paraben/silicone groups or pro-paraben/silicone groups, unfortunately)
Sunscreen is ALWAYS necessary, even if you don't sunburn. Light and oxygen are the number one causes of skin aging. Apply every day unless you aren't going to see ANY sun (even through a window). I don't follow this rule either, it's a hard habit to get into... but I'm trying! And honestly, even if it wasn't for it's superficial effects it's worth doing in order to avoid getting skin cancer. There are no "natural" sunscreens. You may be able to find something that is just zinc oxide (the primary ingredient in sunscreen).
If you truly want an all "natural" regime, here's what I suggest:
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water: it's important to introduce water to the face at least twice a day. Follow up with toner -> moisturizer -> sunscreen. You can use a fragrance and alcohol free cleanser (I can't think of any "natural" ones atm) after rinsing with water to wash away dirt and oil.
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toner: helps balance your skin's pH after increasing it due to water (water is pH 7, skin is more around pH 4-5). Diluted apple cider vinegar is a good toner. Use a 50/50 ratio of ACV to water. Make sure to use RAW and UNFILTERED (Braggs is a popular brand). I do not recommend rosewater as a toner because rosewater is literally roses in water, it does not change the pH of the skin.
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mechanical (physical) exfoliation: should only be done as tolerated, but regularly. See what your skin responds best to. I do not suggest using oatmeal as a mechanical exfoliant unless you blend it finely in a blender. With such large flakes you are bound to scratch your skin too much. Same thing goes for crystalline substances such as sugar and salt (I think they are too harsh for the face, especially for regular use). Ideally, you're looking for as fine a scrub as possible. I've heard rice flour is great for this. I find most people exfoliate 1-3 times a week; I exfoliate 4-5 times a week very lightly and I've had no problems. Exfoliation would be done after washing with water, before toner.
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chemical exfoliation: this isn't "natural" but is your best bet for truly ridding yourself of acne. Chemical exfoliants are alpha or beta hydroxy acids. You may know these as retinols or salicylic acids, respecitvely. Benzoyl peroxide is sort of an exfoliant as well, though it's more of an antimicrobial substance. Each has different properties and are best for certain kinds of uses. For people our age it's better to stick to salicylic acids and benzoyl peroxide because retinols can be harsh on the skin. CeraVE makes some fragrance free moisturizers with SA (I've only found the body one, try and find one made for facial use). You can buy BP pure but it's VERY drying so I suggest keeping the percentage low (2-3%). Some make a whole regime out of BP and use super high concentrations (10-20%); I'm hesitant about it.
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moisturizer: unlike what was said above, many oils are GREAT for the skin, even those prone to comedogenic breakouts. You should really only be using 5-10 drops for your entire face, tbh. A very, very light layer. Did you use almond oil, or sweet almond oil? Sweet almond oil has some great properties for the skin. You should use cold pressed, extra virgin, and organic if you can find it. Other great facial oils: coconut (warning: can be comedogenic), argan, jojoba, maracuja. Avoid essential oils, which tend to be phototoxic (react in sunlight). I love argan oil, myself -- a good quality argan oil is pricey but will soak in within
minutes.
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masks: not 100% essential but fabulous if you want soft, clear skin. A basic mask foundation is clay (bentonite or kaolin are best) and unscented, alcohol-free toner (diluted ACV may work here, but your best bet is to just buy one). Honey is a great ingredient to add into a mask because it's a good emolient (read: moisturizer) and has antibacterial properties. Use raw honey if you can find it, or otherwise as pure as you can get it. Oats are great in a mask as well in order to thicken up the paste. Mix it all up in a NON-PLASTIC bowl (more clay for more oily skin, less for dry skin), apply to face, wash it off when it begins to dry (any longer will just dry out your skin). Then toner -> moisturizer.
I know this is a long post, but your skin sounds a lot like mine so... good luck! I'm free to PM or ask here if you'd like to talk more about skin care.
(P.S.: nice skin is not feminine, but even if it was, trust me when I say anyone you want to attract will looooooooove your nice skin).