Hi spears11- welcome!
So you are walk/running a total of 10-12 miles a week? Depending on how much you weigh you are probably burning 1500 calories or so a week, which equates to just under a half a pound loss. BUT (and it's a big butt) in order for that to work you have to be eating at or below the number of calories your body burns through daily activity. It's a "simple" formula in theory, but hard to do in practice. I know that personally for me, even if I think I am not eating much, if I track my calories I find that I am almost always going over what I need, and couple of miles a few times a week isn't enough to counteract it and see a weight loss (especially if you are hypo and have trouble losing weight in the first place). So my suggestion would be to figure out how many calories you burn in a day without excercise (known as your AMR), and eat a little less than that number. That way you get some loss from a food decifit and some from the exercise. There is a good group on here called "Running for Weight Loss" that can help you figure out your numbers.
But the good news is that you are getting yourself out there and moving! The running will get easier the more you do it (and once the temperature outside starts to get cooler, assuming you live in the Northern Hemisphere). You have a great goal of mixing running and walking several times a week. That's a very realistic approach and one that should help ease you into running. Plus if you can already go 3 miles, you could try run/walking a 5K. The race atmosphere might help give you more motivation for sticking with it.
Glad you have joined us. I know how tough it is with hypothyrodism to have the energy to run and lose weight, but stick with it! Every step you take helps!
Thank you so much Shaunna for the encouraging words. I need them! It's so nice to know that I'm not the only one out there who struggles with this and I definitely have a hard time losing weight! I think you're right in that it will be easier once it cools down. I haven't heard of AMR so apparently I need to do some more research. I will definitely join the other group that you mentioned. Thanks again for all your help!! I REALLY appreciate it!