Opposition leaders claimed Scots are fed up hearing the SNP "prioritise" the constitution, while NHS operations are cancelled and poorer Scots struggle to get into higher education.
But Ms Sturgeon insisted she will "not apologise" for standing up for Scotland's interests during the Brexit process.
Tory leader Ruth Davidson hit out at nursing cuts and said this is having a "real life impact" in Scotland hospitals.
Ms Davidson raised the case Inverurie man Hugh Falconer who was given an urgent referral for treatment last year and was assured he would get surgery in 12 weeks.
But Ms Davidson added: "We've now been informed that Aberdeen Royal Infirmary is no longer able to book his operation and has also stopped referring patients to the Golden Jubilee in Clydebank.
"He's been told that he will not get the operation that he needs. This is on the back of reports this week that in NHS Grampian there are operating theatres lying empty because hospitals don't have the staff."
It comes on the back of report last year which warned the long-term planning had not been carried out to have a sustainable workforce in the NHS, Ms Davidson added.
"They've been at this for a decade so can the First Minister explain why to people like Mr Falconer, who can't get an operation at the same time as operating theatres are lying empty due to a lack of staff?"
But the First Minister insisted that under the SNP staffing in the NHS has increased by 11,500, taking it to a record level.
She added that the surgical team at NHS Grampian has just employed seven new practitioners.
"That is the sign of the commitment we have to staffing in our national health service," she said.
"We are also committed to going further. That's why unlike other parties in this chamber, certainly unlike the Conservative party, we are committed to further investment in the health service."
Labour highlighted figures this week warning that a child from a poorer background in Scotland is more likely to suffer from poor health than a child from a wealthier area. New university figures also show that since the First Minister took office, more youngsters from the richest backgrounds are gaining admissions.
labour leader Kezia Dugdale added: “Nicola Sturgeon should stop the grandstanding on Europe and end the games on independence. It’s clear that the SNP's real priority is imposing another independence referendum on the people of Scotland rather than tackling poverty.”
Liberal Democrat leader Willie Rennie added: "This Government is obsessed with independence, not with solving problems in this country."
He added: "This week we hear about college places cut, economic growth being weak and unemployment rising - threats about independence won't solve those problems."
Ms Sturgeon insisted her focus as First Minister was dealing with issues like nursing and getting students into university - but opposition leaders were the ones raising the issue of independence.
"I didn't ask for Scotland to be in the position of facing being taken out of the European Union against our will," Ms Sturgeon said.
"I will apologise to no-one for standing up for Scotland's interests and trying to protect Scotland's interests."