For a baby to have a blocked/runny nose and a cough?

DD hasn't been 100% since starting daycare five weeks ago. The last day of her second week I kept her home because she had conjunctivitis and a seriously snotty nose (as in huge sneezes all over her face every five minutes). She's just never fully recovered It's worse at night, as the night goes on her nose is more and more blocked until about 4am she comes into our bed because it's keeping her up. When she wakes she has a chesty cough.

The annoying thing is, when she's with us for a decent period, like over Easter, she seems to get better. Then she goes back to daycare, and comes home with a funny nose and we're back to square one.

Should I take her to the doctor to help fight this or would it just be a losing battle with daycare?

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