ALSO the WORST thing you can do is to strain yourself for long periods of time on the toilet trying to make something happen. You might give yourself Crohn's disease. If you're constipated, take 3 doses of Metamucil and wait until you have to go.
I have IBS and have the same characteristics of BMs you are describing. Mucus is something that your intestines produce as a means of destroying bad bacteria. The best thing for you to do is to buy some probiotics as a pharmacy, you can take one everyday as a supplement- it will promote intestinal health. Secondly buy some Metamucil and start taking at least 1 to 2 doses per day. It takes about a week to make noticeable differences, but is a natural source of fiber that can be taken every day. It's NOT a laxative, it has many health benefits but it really hydrates your intestines (aka a stool softener). I've been using it everyday for a year now with a lot of success. Try it- really.
The hyperactive thyroid can be causing both anxiety and constipation. I think you can help your thyroid by eating correctly for your thyroid condition. For the constipation I suggest you take a tablet of magnesium citrate around 400 mg every MORNING and calcium and vitamin D at night. Metamucil with lots of water helps some people, but honestly for some people it actually leads to more problems. There is a pill form, and you would need to drink a big glass of water every time you try it. Miralax might be a better product for you. I know you said no laxatives, but these are not true laxatives and will protect you rather than damage you.
Instead of being in a panic over going to the bathroom, keep glycerin suppositories in your bathroom. Then if you are in a bind you can put one in and help get things started. But you want to do other things besides just this.
One food thing to try is stopping dairy. It causes terrible problems for lots of people. Stop it for two week and see if it helps. This includes cheese, milk, and dairy type yogurt. You can use almond milk instead if you are not allergic to that.
Try eating meat only once a day the size of a deck of cards. Chew thoroughly. Ground meat may be easier for your digestion. Eat lots of vegetables and whole fruit with the skin when the skin is edible. Chew it well. Apples are good. Some people get help with prune juice but it is too gassy for me. Take a prebiotic. This may be extremely helpful. This is from a health food store.
You are not alone and this is not your fault. I will send you a message with a link about foods for the hyperthyroid.
Also if it helps at all my doctor mentioned I had a slightly over active thyroid? So if that has anything to do with what's been happening. My doctor put me on a short medication that helped the lining of my stomach which did help me put my mind at ease and relax again but I stopped taking it after a while because everything felt as if it went back to normal.