I have hypothyroidism and recently have the sensation of something being stuck in my throat constantly, could this be related to my thyroid? or

It might be: thyroid enlargement, but that is unlikely while you are on replacement. You should NOT, however, be taking Cytomel (liothyronine) which is T3, acts only for several hours, causes excessive thyroid hormone levels, and can't be measured with standard thyroid testing. Use the brand name T4 replacement, such as tirosint, only and make sure your levels are normal. Consider thyroid ultrasound if concerned.