Is it normal to experience weird blood sugar spikes while taking cytomel (liothyronine)?

No. I hardly remember a single case where thyroxine (or Cytomel (liothyronine) for that matter) is having any impact on blood sugar levels. If the reason in taking Cytomel (liothyronine) is autoimmune thyroiditis, then theoretically there is a risk of developing auto inflammation in the pancreas (about 10-15% of type i diabetics will develop autoimmune thyroiditis). Please discuss this with your endocrinologist.