Yes, you can use both, but never at the same time — calcium blocks levothyroxine absorption, so the NHS and MedlinePlus say to separate them by at least 4 hours and check timing with your pharmacist.
Calcium (supplements like calcium carbonate, and calcium-containing antacids such as Tums, plus calcium-rich foods) binds levothyroxine in the gut and reduces how much of your thyroid medicine your body absorbs. MedlinePlus advises that if you take calcium carbonate (Tums), you take it at least 4 hours before or 4 hours after your levothyroxine. The NHS gives the same guidance, noting calcium tablets and calcium-rich foods (milk, cheese, yoghurt) can reduce levothyroxine absorption and that you should leave at least 4 hours between them; the NHS also lists antacids as something not to take at the same time of day. This is a timing/absorption problem, not a toxic combination — the risk is an under-treated thyroid, not poisoning.
Take levothyroxine on an empty stomach, 30 minutes to 1 hour before breakfast, and keep calcium supplements, calcium-containing antacids, and large calcium-rich meals at least 4 hours apart from it (the same applies to iron supplements, which both sources flag). A common routine is levothyroxine first thing in the morning and calcium later in the day. Tell your doctor and pharmacist about every supplement and antacid before starting, because they may want to re-check your TSH blood level after any change. Watch for signs your thyroid is under-treated if you've been taking them too close together — tiredness, weight gain, feeling cold, low mood, or constipation — and ask your prescriber if symptoms return. Do not stop or change your levothyroxine dose on your own; if you're unsure how to schedule the two, your pharmacist can advise on the exact timing.
This is general reference, not medical advice, and not a guarantee of safety. Interactions depend on your doses, health conditions, and other medicines. Always confirm with your pharmacist or doctor before combining products, and follow the dosing on each label.