Extremely clingy, needy pre-schooler! Help!

DD1 was born needy. She cried so much in the beginning and always needed constant attention. So she always got it. DH and I are struggling to understand what is going on with her though. She will be 4 in 3 months time but yet doesn't act like a normal 4 year old. Not the ones I have seen anyway. She cries if we leave her for a second. DH got out the car to put petrol in today and she started crying that she wanted her Dad. We were at the pool yesterday and I walked away to swim while she sat with her Dad and sister and she started crying for me. She could still see me. If we go to dancing class, she refuses to dance on her own, I must be holding her hand all the time. All the other kids dance on their own. She won't play on her own or do anything on her own. I am worried that it is more than just normal child behaviour and she has some sort of anxiety issues. What can I do?