Can I still file 1098-T for years I've already claimed tax return? What a difference it will make by sending my 1098-T to IRS?

We do not know what tax years you are referring to unless you tell us.  You can only amend for a tax refund now for as far back as a 2016 return.  If you were someone else's dependent for those years, you cannot get education credit on your own return--the person who claimed you could get the credit.  If you were not a dependent, then the only way for you to find out if it makes a difference is to prepare an amended return and see.  We cannot see your tax return or access your account to tell you what kind of difference it would make.

https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed?jump_to=answer_3288565

A 1040X cannot be e-filed.  It must be printed and mailed.  It will take about 3-4 months for the IRS to process an amended return.  It is a good idea to use a mailing service that will track it, like UPS or certified mail, so you will know it was received.

Wait about 3 weeks from mailing and you can check the status of your amended return:

https://www.irs.gov/Filing/Individuals/Amended-Returns-(Form-1040-X)/Wheres-My-Amended-Return-1

https://www.irs.gov/filing/individuals/amended-returns-form-1040-x/amended-return-frequently-asked-questions

https://ttlc.intuit.com/questions/1908543-do-i-need-to-amend