You need a light fluid moisturiser for dehydrated and oily skin as putting a moisturiser for dry skin on oily skin is only making it oilier. It may be that your cleanser is stripping your skin and causing the dehydration and sensitivity too.
Oily skin needs a moisturiser to 1.keep the skin balanced e.g with essential oils/other ingredients that encourage the sebacious glands to produce less oil and 2.hydrate but water based not oil based.
Tightness and flaking on a spoty skin is not dryness it is dehydration.
When you say your skin is sensitive what do you mean? do you mean you have used a product and your skin has reacted? if so it may be an allergy to an ingredient (see huberella's comments). On the other hand it may be that your skin has become sensitised from using products that are too agressive (also see hubarella's post). In this case just removing the irritation will cure this problem and you can treat your skin as oily not oily and sensitised.
Real sensitive skin is fragile and therefore reacts to the internal and external environment with a over reaction from langerhans cells (the ones that protect the skin with a histamine response). This means it becomes flushed easily, can react to pressure e.g cleansing and massage and also usually has fragile capillaries as a result of the reactions. If this is the case with your skin you will need to treat the sensitivity first and then tackle the spots.
Just to clear it up for anyone who is interested or wondering about their own skin, the following is a brief summary:
Oily skin has open pores and can have open and closed comedones (white heads and blackheads). You can see an oily shine on the skin. In the more extreme cases it becomes acne. These acne skins are graded by the severity of coverage by spots/cysts. On the plus side it usually stays more youthful although people with dermal acne can end up with scars. People with this skin type do not suffer from dryness but dehydration.
Dry skin has tight pores, can be rough in texture with a build up of dead cells and can also be flakey. It becomes lined more easily. This is actually a relatively rare skin type, people sometimes confuse dry skin with normal skin that has become dehydrated skin, or combination skin/oily skin with dehydration.
Sensitive skin has been explained above. You can test for it by pressing the forehead and seeing if the red colour remains for longer after the pressure and also by looking for fragile capilaries and asking about skin reactions.
Normal skin is neither oily or dry it is balanced and glows-these people are lucky monkeys
Combination skin is just what is says on the tin. Combinations are: normal/oily, normal/dry, sensitive/oily, sensitive/dry.
Any skin can become:
Dehydrated skin- this skin is easily confused with dry skin as it is also tight and flakey however this dehydration can be seen by gently pushing the skin together and looking for fine greyish lines (slightly like scales). This is clearest on the forehead.