Weight gain/inability to lose is a common hypothyroid symptom. It's very possible that once you get your thyroid levels in control, you won't need the phentermine. Actually, a healthy diet and adequate exercise should take its place, anyway, since most people who take weight loss drugs, regain the weight as soon as they get off the drugs.
Levothyroxine should be taken first thing in the morning on an empty stomach, with a full cup of water. You should eat or drink nothing else for at least 30 minutes to an hour. Other drugs should not be taken within a couple hours of the levo.
What were the actual thyroid tests performed and their results, including reference ranges? What dose of levo did your doctor start you on?
Since it takes 4-6 weeks for the levo to reach full potential, it's unlikely that's what's causing your headache and feeling bad, unless you are reacting to the fillers/binders in the med. It's also not unusual for patients to report feeling worse for a bit after beginning med.
I don't know what phentermine is, but there will be no probs taking levo with methadone, as long as it's not at the same time... levo is taken on an empty stomach with nothing for 30minz to an hour afterwards..
Apparently side effects will subside over two weeks when taking levothyroxine, or it could be that he's started you on to high a dose.