As a first time mom myself, I felt totally inadequate at first. I could never put my finger on why, but most of the parenting books I read made me feel even more inadequate and guilty for some reason. But my pediatrician was great and convinced me that I was doing a great job raising my daughter. It's very natural to worry, but fortunately you found this site. People answer everyone's concerns so quickly and I haven't seen any bashing, which is amazing.
My daughter spiked a fever every time she was teething. She acted really sick one time so I took her in and the doctor showed me her gums. She was teething alright and her poor gums were all red and swollen.
As long as it's not a high fever 100 or 101 (I can't remember what age that changes from 100 to 101), you can just give baby Tylenol and be OK. My pediatrician gave me a chart for dosage from 6 mo. to 2 years. Does your pediatrician have a nurse hotline? Maybe yours will give you the dosage info over the phone.
In addition to your pediatricians nurse, most areas have a general nurse helpline that can address some medical questions as well. And I got to know one of my local pharmacist who also had young children and she was very helpful answering a lot of my questions too.
For the teething, I put a half dozen pacifiers in the freezer and kept swapping them out as needed. Even after my daughter was weaned off the pacifier, she still used them only when teething. You can also put frozen grapes or strawberries in one of those cloth strainer rings to suck on. I even tried a suger free frozen popsickle once. It made a mess but I think it made her day.
Hope this helps. Good luck.