Hi Op,
It is possible there is a thyroid problem, but it's important to remember that weight isn't the definitive symptom. Have your read the symptom list on patient co uk? Being constipated is another common symptom, feeling very cold, brain fog, water retention (puffy ankles) hair loss (diffuse) and muscle weakness are all key symptoms (there are more but these are the ones I notice).
I've been hypothyroid since I was 20, now nearly 40. I do need to point out weight gain isn't definitive - at my worst I loose weight, as the muscle weakness it causes, actually reduces muscle (myopathy). I loose my appetite and do not naturally carry much fat except on my bottom so just waste away. The 'weight gain' caused by hypo is slight, and mainly water retention. The weakness though leads people to do much less (including small extra bit of calorie burn eg fidgeting) and crave sugary things and so if appetite doesn't dwindle, they do gain weight.
I do also know from recent bitter experience that a good thyroid level is nothing without a good ferritin - ABOVE 70. At 50 I seem to start to crumble. It can go as high as 200 I think so getting to 100 is fine.
HOWEVER, as I said first of all, it's not unreasonable at all to get a thyroid test. Just don't focus on the weight being the main indicator.
Tsh is the first point of call as it is the most stable result and gives a picture of the whole 'thermostat' mechanism. It's when it's borderline or a little raised but still within guidelines (though these are debatable) that other tests are helpful, if your GP is open minded and helpful.
Weight is reliant on so many factors (even gut bacteria, other changing hormones etc). It's worth ruling it out, but the low ferritin could be as to blame in that it's making you less energetic.
Do get your thyroid results if tested, and do come back to post them here.
The British thyroid foundation have lots of useful info, as do Heath unlocked and thyroid uk.