I didn't want to leave you hanging, so here's a site you can try...Seventh Day Adventist Clinic and hospitals are not religious oriented and I always found their prices to be reasonable.
http://en.wikipedia.org/wiki/List_of_Seventh-day_Adventist_hospitals
If this has not transferred well, just go to google (or whatever) and type in Seventh Day Adventist, Tokyo, Japan
Saw the picture of your dau and she is gorgeous...if you have married a local Japanese, all the more reason he should be more sensitive to your situation. Good luck.
First thing, have your husband find you an English speaking dr. NOW! Especially in Toyko--they have to be everywhere!! ...and if he won't, do it yourself. Get yourself a book for English to Japanese that helps with translation.
You failed to mention whether or not your dau had a fever.
I am not familiar with Japanese docs having only taken my dau to one twice, (she didn't like him and cried which was unlike her so I changed) but I would follow his advice for a day and see what happens. A child must be comfortable with a doc. You not only have the stress of living in a foreign country and not speaking the language but having the added stress of having a child sick and not being able to communicate with a doc--it's too much to ask of i.
If the vomiting continues and she is in distress I would find a doc that speaks English....they are everywhere. Besides I can't imagine a doctor not speaking English, nor can I understand why your husband would even consider putting you thru the distress of not having a rapport with a person you could communicate with. Have him find an English speaking doctor NOW for both you and your daughter.
I have lived overseas in multiple countries and never had trouble finding English speaking docs. What people aren't aware of is the Seventh Day Adventist Clinics have (both medical and dental and in some places, hospitals) all over the world. Check it out on your computer.
I don't know what your living conditions are but you must be independent and proactive in the care of both you and your child's health.
YOU are in a perfect spot for learning Japanese...you are in Japan AND your husband speaks it--so start learning. It's can't be too hard. I took Mandarin Chinese before going to the Far East and local people are not only delighted that you are attempting to learn their language, but are always ready to help you. Be positive that you can do it--if it is only a few basic words. That will help. It will make your life there so much more enjoyable.
Meanwhile, you should not be forced to see a non-English-Speaking Japanese doctor when you don't speak the language. What were you and your husband thinking? He speaking Japanese only is not enough!
If my words seem harsh to you, please forget me because I mean you well and I think you have not been given good advice for living overseas!
Surely there is someone among your husband's friends who has an English-speaking wife who will be glad to help you.
Good luck.