Hello,
From your symptoms you might be pregnant.
Menstruation does have various side effects in different people, including nausea, vomiting, loose stools and back ache. But, no periods and increased nausea and vomiting suggests you could be pregnant. Usually vomiting and nausea is common in 2nd trimester more than 1st trimester. But, it varies from person to person.
I suggest you do a urine pregnancy test, and test if you are pregnant. If you are pregnant then vomiting and nausea is normal. But, if it occurs to an increased extent that you cannot eat anything at all, I suggest you consult a gynecologist.
If you are pregnant, then you need to know about the ANC care in each trimester. There are help groups for ANC care.
Thank you.