Hi @dezibella, Welcome to Connect. You might want to discuss this with your doctor but I think the answer is no even with oat milk as it contains some calcium.

"Can I have oat milk after taking levothyroxine?
Dairy products—including milk, cheese and yogurt—contain high calcium levels, which affect how levothyroxine is absorbed into your body. Drinking milk or eating other calcium-rich foods less than 4 hours before or after taking levothyroxine can reduce the absorption of the drug, lowering its efficacy."
--- How long after taking levothyroxine can you drink milk?: https://www.drugs.com/medical-answers/long-after-taking-levothyroxine-you-drink-milk-3562483/

Are you able to call your doctor?