late to the party here, but
yes it could be teething (when I was a kid the doctor always pooh-poohed my mom about teething fevers but the nurses always waited until he left the room and then told mom, yes, a lot of kids get those ;) ),
or, if you are vaccinating on the recommended schedule, might it be a reaction to vaccines? The three feverspikes over 2 months is why I thought of that. My first had a febrile seizure from a vaccine-caused fever, right around 4 months old.
I'm glad it sounds like you aren't getting seizures :). (We only had the one.)
This is counterintuitive, but I've found that getting the kid (or myself) into a hot shower (whatever feels "warm enough" to the kid) when the fever starts to climb helps ... I think because my body then doesn't have to create its own heat, and can do whatever else it's trying to accomplish (presumably some other immune stuff) ... anyhow, I've short-circuited several fevers that way since figuring it out a few years ago. At 5-1/2 months, she is probably too young to do that safely, but you can store it in your Momma's Tricks for later ;).