I feel like I have a lump in my throat. My mom had to get her thyroid removed. Should I be worried?

Neck lump. Yes - any 'mass' or lump warrants explanation. It should not be ignored. Your mother's thyroid history may or may not be relevant. Please seek attention by your md.
Stricture. Probably not related to your mom's thyroid problem but should get checked by endoscopy.
Dr. can check throat. Thyroid disease can run in families sometimes. Many thyroid diseases are autoimmune disorders, so doctors can check blood tests for thyroid hormone levels as well as for antibodies against one's own thyroid gland. There are other reasons for "lump in the throat" sensations, such as anxiety, swollen tonsil, enlarged lymph node, etc... A primary dr., an ENT dr., or an endocrinologist can evaluate.