Been having breast discomfort for awhile now. Is it because they're too big? I'm 23, 40d, obese, & have no family history of cancer. Can I get mammogram?

Cystic change. You are most likely experiencing fibrocystic change. You can check my prior posts on this subject. You are also probably wearing the wrong bra size. Try a store like nordstrom or intimacy for a proper fitting.
Not necessary. Mammograms are generally not recommended for women under 40. The breasts have increased (dense) glandular tissue limiting detection of abnormalities in younger women. If the pain is focal, ultrasound would be helpful. Pain is an uncommon presentation of cancer, especially in such a young women.
Unnecessary . While the size of your breasts may challenge a mammography center, it is more than do-able. Nevertheless, we rarely will perform mammograms on someone in their 20's.Breast pain is often due to cyclic changes in hormone levels & is best evaluated by a breast surgeon.If an imaging study is indicated, an ultrasound is a better test at your age.If you desire a breast reduction, see a plastic surgeon.
Not necessary. Breast discomfort can be related to different conditions like hormonal, anatomical, even some food like coffee/caffeinated beverages can cause beast pain. Breast cancer, although can , but not commonly, be initially presented with breast pain. Mammo not something is necessary be done at yiur age. In addition, the sensitivity will be inferior due to your breast density. Choose a good supportive bra.
Yes, after Dr. exam. The odds are that you are suffering from a non-cancerous condition. See your gynecologist or primary care physician for a physical exam. Obesity isn't helping either. Obesity is a serious chronic health risk for more conditions than can be listed here. Find a balanced diet plan you can follow for life, and find a form of exercise that is fun for you, pact with a friend, & give it #1 priority.
Many causes for. Breast pain. Large breasts can be painful due to the weight of the breast on the chest wall. Caffeine is a common reason for breast pain. Ultrasound may be more useful at your age. See your doctor for the proper evaluation.
No mammogram. I have reviewed the answers as requested. A mammogram is not indicated. At this time and ultrasound is not indicated. Do address obesity. This is serious problem which will lead to many other problems including increasing your risk for breast cancer. Until you loose some weight, do consider a different bra. Do get an exam from a doctor or nurse who has experience giving breast exams.