When I was in college I did this. I kept getting strep everytime I turned around. I finally had my tonsils out. Now 15 yrs later and I have not had strep or even a sore throat since. Dont get me wrong allergies draining still can irrated my throat but thats it.
So when my daughter was 8 and went threw this. Seemed like she would get strep and a month after being off meds she would get it again. She missed so much school it was crazy. So I took her to an ENT and his comment was, "Yeah, we can take her tonsils but its not necessary if antibiotics work". I actually pushed the issue, just cause I remembered what I went through. So that spring break we had her tonsils out. She did great and loved all the ice cream she got to eat. She did complain about the pain meds burining when she swolled but that was it. Shes now 10 and hasnt been sick since. It was the best decision ever. And if either of my other 2 start having this issue, I would do the same.
For a 3 yr old, it might not be the best just because she might not understand why her throat hurts and she might be very cranky for a few days. But I suggest it this continues on. I would have her tonsils out before she starts kindergarten. I have heard that the younger you are, the easier it is on the kid. Good Luck and just go with your gut on this. If you gut says dont, then dont. If your gut says yes, then press it. Which is what I did.