@cameronmarae
The Murad Clarifying Cleanser is drying and full of irritants; it's not doing your skin any favors. It's not that it doesn't exfoliate...it's that it's drying your skin out quite badly, and the rest of your routine can't compensate for that. BHA is a magical ingredient for blackheads, but I'd rather see you using it in a leave-on form instead of a drying cleanser. As for The Ordinary Peeling Solution, there's a balance you need to find...use it too often and it overdries your skin, exacerbating the peeling instead of clearing it up. And if you've never been regular with exfoliation before, it may just be too much for your skin...something that strong needs to be worked up to. For most folks, frankly I'd rather see a gentler AHA used on a more regular basis instead of a ridiculously strong formula.
As a fellow oily, acne-prone gal, here is my basic PM routine. I have a large sample stash and rotate some items in and out fairly regularly, but these are all great starter products, and I'm trying to stay budget friendly with the recommendations 🙂
Cleanse: CeraVe Foaming Facial Cleanser. Cleansers don't have to be fancy or expensive, they just need to cleanse well without overdrying or stripping the skin. This one isn't just good, it's great.
If you are wearing makeup or sunscreen (and you should be wearing sunscreen daily) you'll really need to consider double cleansing (oil/balm first, followed by a traditional cleanser). Clinique TTDO balm is fantastic as a first cleanse. Wipes or micellar water could be an ok sub, but I really prefer a good balm or oil over those.
Tone: I like an AHA toner daily to control the flakies. Start off once or twice a week, then build up as tolerated. Derma-E Glycolic Radiance Toner is a good budget option, or check out FAB Radiance Pads.
Treat: Salicylic Acid, aka BHA is your best friend for blackheads, and works best as a leave-on. I adore Paula's Choice (she has many formulations, from 1-9%; I use Resist 2% daily and the 4% once a week. 2% is a good starting point for many, and I think you'd be ok with it). For a more budget-friendly alternative, check out Stridex pads.
Moisturize: moisturizers are important for everyone, even us oily folks. Look for lightweight options. Clinique Dramatically Different Gel, CeraVe PM Facial Moisturizing Lotion, and First Aid Beauty Ulta Repair Face Moisturizer are all excellent choices.
A couple of times a week, a clay or charcoal mask can help with soaking up excess oil as well. I really like all of the ones from the L'Oreal Pure Clay line.
That's a basic night routine...I also use essences, vitamin C, and retinol, but those are above and beyond what you need to get started on the basics. If you try a routine like the one above, and find you are still a bit dry/flaky, consider adding an essence (ELF's is excellent, with niacinimide, which is also a fantastic ingredient for pores) and/or a hydrating serum (check out FAB's; it includes peptides, which are fantastic for everyone). I've also found that 2-4 drops of facial oil mixed in with my moisturizer does wonders for helping to control my oil.
For my AM routine, I would recommend an even lighter cleanser (like CeraVe Hydrating), non-acid toner, hydrating serum in the winter, moisturizer, sunscreen. You can add other items, like vitamin C or anything else you might want later, but get the basics down before going all out. 🙂
Add new items one at a time, at least two weeks apart, but preferably 4 or more. It can take some time to see how one product works for you. Also, if you throw several new items at your face and start having troubles, you don't know which product is the culprit. It can take some work (and some frustration...I've been there), but the results are worth it once you figure out what works for you. Good luck!