Would scleroderma or another autoimmune disease cause a lumpy/bumpy texture underneath the skin all over? can only feel, not see.

Doubtful: Without external skin changes, scleroderma is unlikely. A physician would have to examine you to see whether there is abnormality of subcutaneous tissue diffusely. I am also dubious of the presence of systemic disease based only on your description, but if your physician agrees there could be pathology, he/she would refer you to the proper specialist.

Yes: This is called calcinosis. Sometimes the bumps can break through the skin, leaking a chalky material. This can become infected.if you injure the area.