Welcome to the forums.
A 2003 large multinational study found that 25% of localized patients (includes morphea) had at least one other manifestation, such as osteoarticular, neurological (epilepsy, headache, peripheral neuropathy), ocular, vascular, gastrointestinal (heartburn), respiratory, cardiac, or renal. Less than 4% of the morphea patients had more than two non-cutaneous (non-skin) manifestations, and none of the patients in the study developed systemic scleroderma during the follow-up.
I happen to have both systemic and localised scleroderma but, as already said, that is pretty rare. I know lots of people with systemic scleroderma, a few with localised but I don't know any with both other than myself.
Sclerodactyly is a tapering deformity of the bones of the fingers, defined by tight, stretched, wax like, hardened skin on the fingers and hands, causing the fingers to curl inwards, frozen in a clawed position, the sclerodactyly hallmark. Underlying soft tissues can atrophy and depending on severity, sclerodactyly can cause disability. In scleroderma, sclerodactyly onsets with puffiness (swelling, edema) of the fingers or toes, and only rarely advances to the clawed condition described above. It is associated with systemic scleroderma not localised.
Perhaps you might find a way to extinguish all or most of your fear because it isn't doing a thing for you and so far, you don't have any actual red flags. Yes reflux can be a non skin manifestation of morphea but it can also be just one of those things millions of people have and let's face it, odds are in your favour that this it is most likely. Your patches could be anything, including morphea and if they are that, you'll be relieved when you consider that they're not one of the alternatives, such as systemic scleroderma.
And what if you did have morphea and/or went on to develop systemic scleroderma? Unlikely in the extreme but for the purposes of what I am saying...people still live very good, albeit very different lives, with systemic scleroderma. Remember, the only thing that is actually the end of the world is the end of the world. At this point in time you have too many things on your side to invest that much of your time and energy into worrying about something that may never happen and anyways, if it did happen it's not the end of the world!
Let us know what the rheumatologist says and take care.