Fever in elderly

I would like some feedback from seasoned LTC nurses please!! I just started my job on 3-11 at a LTC facility that is 250 beds and completely full. There is one RN and one CMTor LPN per unit and each unit has 50 residents. Yesterday was my first day of orientation One of my residents, an 80 yr old male is being treated for a UTI and is on ATB but he had a temp of 99.1 at the start of the shift. My preceptor said not to give him any Tylenol because he had too many blankets on....well the resident refused the tyl anyway because he said he felt sick from taking his liquid morphine. I documented this and told him I would monitor his temp. At the end of the shift, literally the last 15 mins, I rechecked him again and this time his temp was elevated to 102.3....he agreed to take Tylenol and he did have about 5 blankets on him and I removed all but one. I gave him the tyl and a cool compress and told the oncoming nurse what was going on. Should I have called the the doctor myself? This facility has a strict policy on overtime so I needed to clock out. I felt since I discovered the elevated temp it was me who needed to take care of the problem. I DID intervene, but worried that I will be in trouble if the oncoming nurse didn't follow up.... Any feedback would be greatly appreciated!