Just try giving her infant gas drops, and see if it helps. It really helped my daughter, who had BAD gas problems.
Also, yes, she could be teething. Look in her mouth.
Or, she could very possibly be going through a 'growth spurt' and simply IS hungry and NEEDS to be nursed or needs a bottle. This is okay and normal.
Or, it could be the cows milk that causes gas? For my sister, she gets gassy sometimes with milk. Sometimes. Not so much that she has to stop drinking milk...but just sometimes it happens.
But, I know that gas is painful and wakes babies. You probably notice her farting when you pick her up and rock her in the rocking chair, because this 'motion' is helping to get gas circulated and expelled from her body...thus she is 'tooting.' It would be the same as if you massaged her tummy, this would help as well. Or, bicycling her legs while on her back. This also helps gas.
And, some babies just take in a lot of air as they eat or drink throughout the day. Each child is different.
I would try the infant gas drops first... then see. This really helped my daughter, who is just a 'gassy' type like her Dad anyway.
All the best,
Susan