Can you give mucinex and Claritin at the same time?

Yes. Drink plenty of fluids. Use Tylenol, aspirin or an NSAID for fever or headache. This applies to Claritin (Loratadine) and not Claritin D (Loratadine with Pseudoephedrine)

For Claritin D Yes. These medications each contain two drugs that treat two different conditions. Mucinex DM is an expectorant/cough suppressant. Claritin D is an antihistamine decongestant. Avoid Claritin D if you have high blood pressure or heart problems. If you develop a fever, take Tylenol (acetaminophen) or Motrin (ibuprofen) with any of these.

Source: http://www.bjchealth.org/?id=5488&sid=3