First of all, no household with kids should be without a decent thermometer. This will be an issue for years and years (i.e. does my daughter have a fever?), and so, I suggest you invest in a good thermometer that you feel comfortable using. My wife and I bought a digital ear thermometer because they are fast, accurate (assuming you use it right) and easy to use on infants and toddlers alike. Rectal thermometers are the most accurate, but lots of people are squeamish about that, and, it can be tricky to be sure you have obtained an accurate measurement. The reason I say this is that I have been surprised how many times I was convinced my now 2.5 year old son had a fever by touch, only to find that I was wrong (by taking his temperature).
That said, you really shouldn’t take any chances with the health of a 3 month old baby. A fussy baby with a temperature could have any number of things, ranging from a simple cold to diarrhea to an ear infection to a urinary tract infection to pneumonia to meningitis. In addition, infections in infants can spread quickly, going from mild to severe in a matter of hours. If she has a high fever and is fussy, take her in for evaluation ASAP. Also, you really should trust your maternal instincts. If you sense something is wrong, then it probably is.
In general, reassuring signs include normal eating/drinking, a normal number of wet/poopy diapers, continued interaction with you and vigorous crying. More concerning signs would be loud coughing, difficulty breathing, new rash, sleepiness, difficult to arouse, poor appetite, and lack of crying.
Finally, there is a lot to be said for the reassurance of a thorough medical evaluation by a pediatrician. You will worry and fret until she gets better, but a reassuring examination will help you feel more relaxed about her health. I hope she (and you) feel better and get some sleep.