Mama,
This is normal! it does not last forever. I just answered a topic on stranger anxiety that really covers all this.
Carry her. Put her in mitts and try having her Dad carry her, but don't force it.
Use a carrier. She is only 3months. She doesn't know anything yet - she is just NEW!
My husband went through this - and didn't hold him unless absolutely necessary. I think it really affected how my son relates to him now. Even just holding him (instead of leaving him in the carrier) would have been better.
I can recommend a Moby at this age - but never outward facing (it would hurt her back).
an Ergo would work well too - if you can get the insert to allow her to sit cradled instead of splayed out. (legs together.)
I would also HIGHLY recommend a visit to the Chiropractor. My son was born c-section. Somehow, he STILL Managed to have something wrong with c1 (the very top vertebrae, still in the skull) being out of place. Find a chiro who is certified for infants. If you need one - she is in Fairport, Dr. Paula Derleth, and now her husband is certified also. A fair hike but for a visit or two - it is WORHT IT. it helped SO MUCH with spit up (and spit up was the heartbreak for me, being a breastfeeder, because it is so much work for me to make all that milk and see it go to waste!)
Carry her. Everywhere. She is needing and craving that sensation of being with you. And please ignore anyone who tells you it is spoiling the baby. Truly the spoiling is done when a baby or child is ignored.
so much more I want to say but I have to go sleep. Good luck,
M.