I'm pretty sure your girlfriend will have to go back to India to adjust her status. If someone from the US got married in the UK on a visitor's visa, they'd have to go back to the US to adjust status (unless they were here on a student visa or work visa worth 6 months or more, which wouldn't apply to your girlfriend).
It sounds like your girlfriend will need another sponsor if she's to come to the UK permanently. If you don't have ILR (indefinite leave to remain) in the UK, you cannot sponsor her.