Boglin
Well considering you hardly wear any makeup and no SPF if all you're using the face wipes for is to remove eye and lip makeup it's not all that damnable of an offence, but you really do need to be cleansing at night. Far more important then than in the morning.
Are you oily with blemishes, or are the blemishes occasional/time of the month related?
I think aside from changing up a few products to more gentle ones and including an SPF you should be looking towards a BHA for the oiliness and blemishes. Probably the Clear Anti-Redness Exfoliating Solution 2% Salicylic from PC (get a travel size version first, introduce it slowly and probably move it up to using every day). In contrast to the AHA (glycolic) you're currently using this will penetrate deeper and help dissolve the impurities (thus reducing blemishes) and clean out pores which will hopefully inhibit some of your excess oil production. I do think it's worth keeping an AHA in your routine to help with the healing and recovery with blemishes.
Have you ever tried LRP effaclar duo? Think it might be worth incorporating for you too, using it in place or with a moisturiser. By the looks of it the Vichy detox is a similar product but the LRP has a better formulation and better reputation with acne suffers.
So in terms of routine, as discussed here today: daily clean flannels (and use a washing powder that won't irritate, no softener, etc.), washing hands before starting your routine, entire routine at the tap, avoiding putting your face near water during showers, changing your pillowcase more often if necessary, etc.
AM :
Cleanse (Burt's Bees Soap Bark and Chamomile or L'Oreal Skin Perfect gel) I'm not sure which L'Oreal one exactly you're using but it doesn't look great so I'd repurpose it, I suggest putting in the LRP Toleriane Dermo Cleanser here, the BB isn't totally awful so I'd finish that up initially.
tone ( L'Oreal Skin Perfect or Nip and Fab Glycolic Fix ) Again rid yourself of L'Oreal, it's an old school harsh toner with a lot of alcohol in it, it's not doing you any favours by stripping your skin further back only to encourage your skin to produce more oil in response. I'd use the N+F at night instead, especially since you're not using any SPF currently. Insert the PC 2% BHA here in place.
serum (superdrug hydrating one) As an oily person it is good you're tackling the dehydration so keep at it, possibly consider the TO HA + B5, though the reviews on this are mixed I do think for those with oil issues it's a good match.
moisturise (an oil free neutrogena one), consider the LRP Effaclar Duo here with or without the neutrogena. LRP Toleriane Fluide also an alternate moisturiser worth considering in the future.
SPF, Biore Watery Essence would be my first pick for you, LRP Anthelios Fluide SPF50 otherwise.
PM :
Don't shoot me but face wipes continue using the face wipes to remove eye and lip makeup and insert an oil cleanser here, DHC Cleansing Oil is probably a good one for you.
LRP TDC (BB's while you finish it up)
then tone - as mentioned above use the N+F Glycolic here if they work for you. It's probably over budget but I would consider getting the Biologique Recherche P50 lotion as it's very good for those struggling with acne/oil control as well as being beneficial anti-ageing wise. It slays spots like nobody else ime. Use it about 2-3x a week, perhaps in your case a bit more often (but you have to build up to it) and start on the P50W version.
serum as above, - you can consider inserting TO Advanced Retinoid 2% here at some point but get the basics sorted first. TO Niacinamide 10% will also help with pores and reducing inflammation. Retinol I would use alternate on nights, glycolic/AHA one night, retinol the next.
Garnier miracle sleeping cream, nuxe huile prodigieuse or vichy night detox As above consider inserting LRP ED here with or without LRP TF. You could also opt to use Cerave PM Lotion (instead of LRP TF) which has a high % Niacinamide in it (4-5) and not get the Ordinary version (though I prefer that one).
So in order of priority, grouped together to buy in different stages. Introduce slowly and spaced apart (w. exception of cleansers) into your routine:
Phase 1
SPF
Oil Cleanser
BHA
LRP ED
Phase 2
LRP TDC
TO Niacinamide 10%
BR P50W
Optional/consider in the long term
TO Advanced Retinoid 2%
TO HA 2% +B5
LRP TF
Hope you're able to understand it all, let it digest and feel free to ask where it isn't clear.