Hello Bedore! Since frog has not pooped for a week and appears it did vomit, take a look at frogs left side (right when looking at frog head on) and see if it looks different and bigger than other. If so, (and specially if it feels hard) could be a constipation problem.
For that get a small tub that fits the frog and fill to frogs chin height with 80F dechlorinated water + a few drops of honey (3-4 for baby is OK). Let her sit there for 20 minutes and then discard the solution and do a rinse of same without the honey. Usually frogs will poop during baths. After baths you can place frog back on her enclosure dish and if it poops you are done. If it does not repeat daily until it does.
Also, recommend as soon as you get some poop to take it to veterinary (hopefully with amphib experience) to conduct a fecal sample and ensure your frog is free from parasites. Good luck!