Due to the COVID situation it is nearly impossible to find filter tips. Is it possible to do it without filter tips by making sure to clean the pipette with RNAse zap before use and working extremely carefully?
I would also add to make sure that you have some no RT controls as well as some no template controls this should let you know if you have any background amplification.
You can clean the pipette with RNAse zap and use autoclaved tips instead. You can exposé the consumables used for qRT PCR to UV light to avoid any DNA contamination. Clean the working table or the PCR hood before commencing your work. Please wear gloves while performing the experiment and avoid keeping tip boxes, PCR tubes exposed to air for a prolonged period.
I would also add to make sure that you have some no RT controls as well as some no template controls this should let you know if you have any background amplification.