It only takes tiny amounts of pcr product to contaminate a reaction and every 10 cycles is 1000 times more product. The contaminationmay come from buffer transferred back from post pcr area and gels or in the pipettes used to handle pcr product.

I would get all new reagents and dilute the new primers with another researchers TE and pipettes. Clean your working area with soapy water and dissemble and clean your pipettes. Meanwhile use another researchers pipettes and working area and pcr reagents and you will get more information as to where the contamination is.

If everything is still contaminated after your major clean up and throw out of your plasticware but pcrs of the same reaction with other peoples reagents is clean then you can solve contamination by designing new primers where one primer is outside your original primer set (larger pcr product) then the contamination cannot amplify and ceases to be a problem

RT-PCR (Real-Time) primers can start showing amplification in NTC (Non-Template Control) after only a few uses because of carryover contamination. Carryover contamination is when a small amount of material from a previous reaction is carried over into a new reaction and can cause false positives. This is often due to improper cleaning of the PCR tubes, pipettes, and other equipment used in the RT-PCR reaction.