When my baby (now 7 months) does this it means he is very tired. I then take the opportunity to put him for a nap and he always falls asleep. I coulnd't beleive my baby needed that many naps but still at 7 months he sleeps 9-12 hours a night and takes 2-3 naps a day.
It's so completely normal for babies to do this, simply because they can, but my son did turn out to be allergic. He never really showed other symptoms of being allergic to our cats, but we decided to have him tested, and low and behold, he was. It broke my heart, and I cried for days because we had to give our cats away, but when the doctor explained that he could develop asthma because of this, we knew we were making the right decision.
It might just be seasonal allergies... I don't know where you are, but here in FL the pine pollen is so bad everything outside is covered in yellow! Try following some basic allergy precautions, like washing all bedding in hot water, putting mattress and pillow covers on the bedding, changing clothing and washing hands/face when coming in from outside, keeping windows closed in the car and house and using air conditioning instead, etc.
I'm allergic to cats, but it's totally under control with a daily Zyrtec. My doc said he would test baby for this in a few months to see if she was allergic, too. She can always take a children's version of Zyrtec. (We have 5 cats... not going to give them away unless there is some horribly debilitating illness that can't be controlled -- they range in age from 14 years to 3 years and are as much a part of our family as my DH or DD.)