Can I purchase a house under FHA that I have lived in for only 3 months?

Do you want to buy the house you have been renting for 3 months? If so, you should have no problem with that as long as you qualify to do so with a review of your credit, income, job history, assets, application. I would suggest speaking with a local loan officer/lender and having them review your information so they can provide you with all of your available options. Best wishes, Sean