Brief Answer:
follow the advises.. maintain a healthy lifestyle..

Detailed Answer:
Hello XXXX, welcome to HCM,
I've gone through your query and understand your concern,

All those symptoms seem to be appearing due to acid-peptic disease (gastric problems), the rotten egg taste is primarily developing due to offensive gas (sulfur dioxide and/ hydrogen sulphide etc.) formation, and a suspected food-intolerance with/without a stomach bug (at the present scenario, given the multiple vomiting and diarrhoea)..

First of all, you need to start taking a PPI medication (antacid) i.e. Cap PANTOPRAZOLE (PROTONIX) 40mg Once daily in empty stomach (15-20 min before breakfast), continue it for at least next 15 days and observe how you stay..

Although it's extremely important to narrow down if there's any particular food product which is responsible for this (it can be anything starting from some barbeque/ sea foods/ milk/ any processed cheese/ any particular asian cuisines/ alcoholic beverages and several others), please try to recall which is one common factor involved in each of those various occasions, as you may be intolerant to some of those food products..

Please stay well hydrated by drinking a lot of water (it's extremely important to avoid any dehydration, since so many vomiting episodes happened ), you can also get WHO-ORS (Oral Rehydration Solution, easily available as OTC), mix it in 1 liter mineral water drink it up gradually over next 2hrs, repeat the same but drink it up in another 6 hrs.. have plenty of fresh fruits, and include fresh green leafy vegetables and salads in your daily diet.

Medicine alone won't be sufficient to resolve the gas problems, please avoid junk/ deep fried/ spicy foods for the time being..have simple home cooked meals.. avoid soda/smoking/alcohol (if you do)..

Eat small frequent meals instead of large portion meals, try to chew the foods properly, do not eat in a hurry, also try not to talk during eating, start practicing to take your dinner 2-2.5 hrs prior to your bedtime..

Start taking Yogurt and curd on daily basis, they are in fact rich in healthy bacteria for your gut functioning..avoid milk in direct form..also avoid certain foods which predispose to excessive gas formation (i.e. Cabbage, cauliflower , turnips, radish etc.).. Avoid fizzy carbonated beverages..take fresh fruits instead of packaged fruit juices..

Follow all these, and let me know how you stay in the due course..

If despite following all these, symptoms don't improve/worsen over a period of time, then I'd strongly suggest to get yourself checked at your nearest ER/urgent care for a prompt check-up (few necessary investigations eg. CBC, electrolytes, Stool routine microscopy and X-ray and Ultrasonography of the abdomen) as well as intravenous fluid therapy (in case too many episodes of vomiting and diarrhea happen, then orally fluid acceptance will be considered inadequate to compensate the fluid-loss, thus other relevant measures have to be considered)..

Take Care
Kind Regards

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