Type 2 Insulin?

Good afternoon I have had diabetes for approximately 20 years 10 years ago I switched to insulin is made my diabetes control much easier however I have a question, can somebody be allergic to insulin I keep getting the same answer you can have sugar lows or hypoglycemia from insulin. I understand this but can you be allergic to insulin. Weird side effects when I take my insulin.

it,s all most like I can feel my body changing almost instantly, real bad jitters, sometimes headache, chest pain the sweats head to foot, this is all within 10 minutes. if you were going from a normal blood sugar to a low blood sugar quickly drastically.
but when I check everything is OK regarding sugar readings within normal range before and after.

Thank you I will try again with my team they keep going to low blood sugar as the effect of insulin, I will suggest they look deeper. Thanks again