If you have dry skin make sure you moisturize even if it's oily moisturize because if you don't your skin has to work extra hard to do it for you.
My suggestion would be to wash your makeup off every single night and
then wash your face with something that will prevent breakouts
then use a moisturizer after wards.

go to the doctors and they will give you some tablets:)

I've never really heard of dry and oily skin together but try Eucerin. It's really good. I know you said you don't like buying stuff but trust me its going to be worth it. It will mostly help the dryness and acne. I recommend the " Itch-Relief Moisturizing Spray" or the original "Eucerin Original Moisturizing Creme" for you. You can find them in Walgreens. There's always small ones for trying.

Here's the website with most of its products http://www.dermstore.com/long_Eucerin_100024.htm

But if you still dont want it then try this website. It gives you helpful suggestions and how can you help it get better daily your own way.

http://www.cosmeticscop.com/all-about-combination-skin.aspx

Im not the best when it comes to skin care but i think the problem is, is that you don't know your skin type to identify good products for you! I personally think you have combo skin (oily in t-zone, but dries out easily)

Daily Moisturizer: Neutrogena's oil free moisturizer with spf 15 ( works great for running since has spf and doesn't make your skin oily!) Also, this product is not tinted so you can put it on at night also!

Acne treatment: Personally I don't have major acne so I wouldn't be one to know all about acne products but since school can cause stress and breaks me out i use Neutrogena's acne stress control ( it hydrates so your dry areas wont get worse and is oil free! also, works quickly and is very effective!) I also recommend any type of acne cleanser ( just don't get super cheap items!)

Body Lotion: Bath and Body Works body lotion is great and smells fantastic! It has vitamin d and is super healthy on your skin! For rashes, bug bites, and extra dry skin try Aveeno's skin relief moisturizing lotion! It is fragrance free and effective for 24 hours!

Maks, cleansers: For a cleanser clean and clear has great cleansers for all skin types so go to there website and check them out! For masks neutrogena ( as you can see im addicted to this line, haha) clear pore cleanser/mask makes is a great mask that prevents blemishes, oil control, and deep cleansing! (this could also be a cleanser!)

So I hope this helps! P.S. These are all drugstore products so they are not really expensive, but they don't work cheap like other drugstore products!

You got me… You may also want to check out http://findsth.info/452097/skin-care-treatment

Here are couple of anit acne homemade masks. They are natural and cheap so you have nothing to lose:
http://www.girlslovestyle.com/2011/04/5-homemade-anti-acne-masks/
Hope it helps:-)