Timid daughter in family

I have a four year old daughter. She lives with my girlfriend, my girlfriend's daughter who just turned 5, and me. My daughter is with us the majority of the time and sees her mom, twice a month sometimes once. My girlfriend's daughter is with us a lil bit more than half the time. They are both quite opposite from each other which is not necessarily the problem, my daughter is very shy and hard to open up with other kids and adults at first and does not have many friends in school while my girlfriend's daughter is a lot more social, and picks up things a lot quicker. My daughter can't seem to pay a lot of attention because it seems she gets distracted quite easy, she is very hyper. I suppose her strenghts are her dexterity, agility and curiosity. My concerns are that she doesn't get to see her mom very often and while I try to do all that I can to be there for her as well as my girlfriend I feel that it's not enough. She looks up to my girlfriend's daughter a lot as a young sibling with an older one but I feel that sometimes she gets bullied by her because she's older. My daughter is very sweet and loving but a bit of a whiner too which gets on my girlfriend's nerves more easily than to mine, so my girlfriend can be a bit harsh with her than with her own daughter. It is a very difficult situation for me because I don't want my daughter feel left out and I want to keep a consistent discipline at home that fits both girls. Should I look for a psychologist in my area and have my daughter seen at to ensure she is growing up appropiately and happy? Any suggestions or questions are welcome.

Thank you very much.