My doctor told me I had a swollen thyroid when I went to see her about a painful lump in my throat, is this serious and connected to my back spasms?

Not related to back. Enlarged thyroids are usually not painful unless there is inflammation (subacute thyroiditis). A thyroid ultrasound and thyroid function tests can help figure this out. Subacute thyroiditis resolves after a few months. Back pain is usually not connected to thyroid problems.