Shortness of breath can be a hypo symptom - I had it pretty bad when I was very hypo, but I don't believe the pain in the left arm, heaviness in the legs are thyroid related. Neck and jaw "maybe", but only if there were large goiter pressing on something essential, in which case that, most likely, would be felt/visible from the outside.
IMO - other things need to be checked out. Hashimoto's doesn't cause the symptoms -- resulting hypo does.
I think your symptoms could also be heart related. Have you had your heart checked?
When I was hypo I experienced some of the symptoms you described.
1. shortness of breath - no. 2. pain in left arm - no. 3. heaviness in legs- maybe. 4. tingling - maybe. 5. electrical impulses - yes. 6. neck and jaw pain - no, but I experienced leg pain. 7. extreme fatigue - yes.
What are your actual thyroid hormone levels, including FT3, FT4 and TSH? Please include reference ranges...
Is it possible you might have had a stroke (pain in left arm, neck and jaw pain)? Even a mini stroke?
Have you been tested for vitamin B-12 deficiency? Do you have diabetes and if so, is it under control?
Please post thyroid related blood test results with reference ranges and we can go from there.