Can my 8 year old take Claritin (loratadine) and ibuprofen together? Not sure if her runny nose is due to allergies, but she has a fever.

Not allergy. A young child doesn't get a fever from an allergic reaction. Tylenol (acetaminophen) or a non steroidal antiinflammatory can help to reduce fever. Antihistamines work well for allergic conditions but not colds or viruses.
Yes. The answer is yes...Antihistamines (claritin, zyrtec, benadryl, (diphenhydramine) etc) and anti-fever (motrin, tylenol) can be taken together. If your child has a fever, it is not likely to be from allergies, however te antihistamines can still be used for sympom relief for upper respiratory symptoms (runny nose, sneezing, etc). If fevers are persistently >100.4, or for any concerns, ask your doctor.