If you are taking some form of Synthroid or replacement hormone for your hypothyroidism, you can take anything. I know of no problems with interactions. I have been hypo for 28 years. Always ask your pharmacist once you have made your choice and that will be your best double check system. Musinex behind the pharmacy counter has 1200 mg of guaifenesin. This is what my doctor always prescribed me until it became Maximum Strength over the counter/behind the counter to get that strength.
I take mucinex which has helped a bit. I also take Benadryl. It helps. I take smaller dosages, but it has helped me.