A B737-700 WAS DISPATCHED IN NON COMPLIANCE AFTER DEICING WITH NO DEFERRED ITEM OR SPD RESTR PLACARD. CREW DISTR BY PAX OUTBURST.

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ACFT ACCUMULATED SOME STRUCTURAL ICE ON APCH TO ZZZ. DURING THE FO'S WALK AROUND; HE NOTICED STRUCTURAL ICE WAS PRESENT AND NOTIFIED ME ACCORDINGLY. I THEN NOTIFIED THE CUSTOMER SVC AGENT (CSA) HANDLING US THAT I WAS REQUESTING DEICE ON THE RAMP. IT WAS SNOWING SLIGHTLY ON AND OFF; BUT THERE WAS NO ACCUMULATION. THE CSA THEN CAME TO ME AND SAID THERE WERE APPROX 6 CONNECTING PAX THAT HAD LANDED AND TRYING TO GET TO OUR FLT. I CONTACTED THE STATION COORDINATOR TO COORDINATE THE DEICE AND HOLD TIME FOR THE CONNECTING PAX. WE AGREED TO PULL THE JETWAY BACK; DEICE AND THEN BRING THE JETWAY BACK TO BOARD THE REMAINING PAX. THE DEICING COORDINATOR INDICATING HE WAS APPLYING TYPE 1 FLUID; AND I ACKNOWLEDGED HIM. AS THE JETWAY WAS BEING BROUGHT INTO PLACE; A MEDICAL EMER WAS OCCURRING ONBOARD. THE FLT ATTENDANTS APCHED THE FLT DECK WITH NEWS OF A 12 YR OLD BOY SEATED; WAS HAVING EMOTIONAL OUTBURSTS (ANXIETY/PANIC ATTACK AS DESCRIBED TO THE FLC). AGAINST THE FLT ATTENDANT'S RECOMMENDATION; ANOTHER PAX GAVE THE BOY A PRESCRIPTION DRUG. THE DRUG WAS SAID TO BE A 5 MILLIGRAM VALIUM; AND THE BOY'S MOTHER ALLOWED IT. MR Y WAS BROUGHT OUT TO THE JETWAY TO GET SOME FRESH AIR; AND THAT IS WHERE I FIRST TALKED TO HIM TO HELP CALM HIM DOWN. BOTH CSA'S WERE ALSO PRESENT. GIVING THE CHILD A PRESCRIPTION DRUG CONCERNED ME AND PER THE REQUEST OF THE FLT ATTENDANTS; MED LINK WAS CONTACTED. ACARS WAS UNABLE TO GET THROUGH; SO I CALLED DISPATCH VIA CELL PHONE AND WAS CONNECTED TO A PHYSICIAN. MED LINK CONNECTED ME TO DR X; WHERE I THEN BRIEFED HIM. AFTER SEVERAL QUESTIONS; SUCH AS; DURATION OF THE FLT; HE RECOMMENDED THE BOY BE REMOVED FROM THE FLT. THE DOCTOR ALSO INDICATED THAT IF; IN FACT; VALIUM WAS GIVEN; THAT WAS ACCEPTABLE AND NOT A CONCERN. I PROCEEDED TO HAVE THE MOTHER; DAUGHTER; AND SON; AND MR Y REMOVED PER THE PHYSICIAN'S RECOMMENDATION. DURING THIS TIME; I WAS IN CONTACT WITH THE STATION COORDINATOR. THE MOTHER WAS VERY CONCERNED ABOUT THE STATION COORDINATOR'S PLAN OF REROUTING THE FAMILY THROUGH ZZZ AND THEN ZZZ1 TO PROVIDE THEM WITH SHORTER LEG SEGMENTS. THEN; I WAS INFORMED THAT THE HUSBAND AND FATHER HAD RECENTLY PASSED AWAY. I THOUGHT THAT STRESS WAS A MAJOR CONTRIBUTOR TO THE SIT. I TALKED TO MR Y ONCE AGAIN; AND FELT THAT HE WOULD BE ABLE TO MAKE THE FLT AND THAT IT WOULD BE THE BEST COURSE OF ACTION FOR THE ENTIRE FAMILY. THE STATION COORDINATOR AGREED WITH MY DECISION. WE REBOARDED THE FAMILY AND CONTINUED TO DEPART FOR ZZZ1. FLT WAS NOW NEARLY AN HR LATE. DURING THE CONFUSION; IT WAS NOT CLR IF TYPE IV FLUID WAS APPLIED; AND I HAVE TO ASSUME IT WAS. THE ACFT WAS CONFIGURED PROPERLY FOR DEICING AND THE ELEVATOR WAS CYCLED 5 TIMES AFTER THE FLUID APPLICATION. I ALSO NEGLECTED TO GET AN ENRTE MEL FOR THE B737-700. DURING THE CLBOUT; CHICAGO CTR REQUESTED AN EXPEDITED CLB AND WE STAYED BELOW 270 KTS; BUT I DID NOT NOTICE IF WE REMAINED BELOW 270 KTS THROUGHOUT THE ENTIRE CLB AND DURING THE TRANSITION PHASE. NO ABNORMAL FLT CHARACTERISTICS WERE OBSERVED. IN SUMMARY; THERE WERE NUMEROUS CONVERSATIONS BTWN MYSELF AND DISPATCH FOR PAX LOADING AND FUEL REQUIREMENTS AND THE STATION COORDINATOR REGARDING THE MED EMER AND HOLDING TIMES AND DURING THE CONFUSION; I FAILED TO ENSURE CLR AND CONCISE COM REGARDING THE DEICING EVOLUTION AND TO FOLLOW THROUGH WITH THE APPLICABLE MEL PROCS.