You ask a good question, but I don't know the answer.
Different doctors use different individual tests to measure thyroid function. Some rely (wrongly so) on TSH alone, which can suffice as a screening test, but diagnosis shouldn't be based on it. Some MDs use archaic tests such as total T4, total T3, and FTI. The best thyroid panel is a combination of TSH, free T4, free T3, and thyroid antibodies (TPO and AG). If your doctor ordered only TSH, the cortisone may not affect that result, but you should probably directly ask him to be sure.
BTW, we had a discussion of frozen shoulder and hypoT here not too long ago. You can search the archives to read about how many of us here have actually had the combination of conditions. Maybe it's only coincidence, but I thought it was very interesting.
"We can complain because rose bushes have thorns, or rejoice because thorn bushes have roses." Abraham Lincoln