I started my period at age 11. i will be 20 in about two months and my periods have always been irregular. is this really normal like my doctor says?

For many yes: Some women are like clockwork every X days and some vary with weeks to months between cycles.Early hormone research was directed at helping women plan for their cycles, the birth control was a side effect. Although the pill is better known for birth control, many in your situation use it to pace their cycles so they become more manageable/predictable.

Irregular menses: There are several reasons for "irregular periods". Stress due to job, school, relationships, can cause ovulation to occur at unpredictable times, resulting in onset of periods from 24 to 38 days apart. More information is needed to give a complete answer, but if your cycles are accompanied by breast tenderness and cramps, it is possible that this is just "normal" for you.