Is a breast self-exam more accurate than a mammogram at 35?

Apples ; Oranges. Mammograms can see things which cannot be felt; breast (self) exam can sometimes find lumps that cannot be seen--these modalities complement one another. That said, we usually do not recommend mamms until age 40. If one has a suspicious lump by either modality, (nonsurgical) needle biopsy is the only means for definitive diagnosis.
Sometimes. In younger women with very dense breast it is sometimes not possible to visualize a palpable nodule on mammo detected on physical exam. In such cases, other modalities such as ultrasound and MRI may be utilized.
Probably not. In the average risk person, breast self exam may be important, but its contribution to breast cancer detection is relatively limited. The sensitivity of mammography is diminished in dense breasts(seen particularly in younger woman), but it is still probably superior to self exam.