Welcome to Thyroid Board
Yes you could have a thyroid problem. To get to the bottom of this you should get a proper set of tests, TSH alone is not enough to assess thyroid function. You should get freeT4 (direct, not index), freeT3 (not uptake or total) and thyroid antibodies (TPO and TG AB, TSI too if you're suspecting hyperthyroidism) tested along with TSH. Get a copy of all of your (thyroid related) results and post them here with their reference ranges (ref. ranges vary from lab to lab so you'll need to know Your lab's ranges), we can have a look at them and give you our opinion. Being "within range" doesn't automatically mean there's nothing wrong with your thyroid.