It looks like your acne could be hormonal. Hormonal imbalances can certainly lead to acne (primarily along the jawline) and oily skin. With oily skin you will then be more prone to getting whiteheads and clogged pores, resulting in that bumpy texture you've described. When your skin gets a lot of excess oil sitting on it, it can become irritated and red, which is something I have personally experienced. You should go to the dermatologist and ask them about some different hormonal treatments that you can try. Oily skin isn't something that can be treated from external treatments - it can be contained but it won't go away if there is something internal causing it.

In the meantime I would try using a gentle exfoliating face wash at night at least 2-3 times a week. Exfoliating can be very beneficial for people with oily skin to get away all of the built up dead skin cells and such that collects on the face. I would also try a face wash that has a little bit of salicylic acid in it, as this is also very good for helping get rid of excess oil and helping with acne. Neutrogena makes a great moisturizer for sensitive skin that is also lightweight and non-greasy. They also make good face washes. I use a lot of their products haha.

If your doc gives you some kind of antibiotic or hormonal treatment, they will probably also give you something topical for your face. It's most effective to treat acne both ways - from the inside and out! But just doing one or the other won't tackle the whole problem.