I'll assume by "stomach", you mean abdominal pain, probably lower abdominal pain. And yes, tampons can cause lower abdominal pain in the presence of endometriosis (ectopic endometrial tissue). The symptoms of endometriosis can include pain on micturition, defecation, tampon or diaphragm insertion, increased pain with menses, intercourse, etc.
Use of tampons in healthy females is generally well-tolerated.
Edited to address OP's edit:
Tampons are generally well tolerated by healthy, normal females. However, there are groups of females that do find tampon use uncomfortable, chief among them adolescents. For this reason, physicians often speak with adolescents at menarche about tampon use.
With regard to comfort, girls often choose tampons of too high absorbency. Highly absorbent tampons may cause discomfort in young girls because of their larger size or because of a drying effect during wear and upon withdrawal. Advise your patient to choose the lowest tampon absorbency for her needs by experimenting with a pad or pantiliner for backup protection. Less absorbent products can be used on lighter days. This guidance is also consistent with the Food and Drug Administration’s current recommendations for reducing the risk of menstrual toxic shock syndrome.
In other words, young girls should use smaller tampons. Pain with tampon use in this age group is more likely and in some cases can lead to problems with pain later on.
Relation between pain symptoms and the anatomic location of deep infiltrating endometriosis
Prevalence and predictors of chronic lower genital tract discomfort Small self-reported study
Menstruation in young girls: a clinical perspective, Obstetrics & Gynecology, Vol 4., 2002