We know that in #LTE downlink transmit uses #OFDM but in case of uplink transmit, OFDM scheme is not used. Can someone explain the reason behind this?

For uplink, lte uses sc-fdma which has relatively low PAPR compared to OFDM. A low PAPR is required in order to avoid high power consumption in the mobile terminal, otherwise battery will drain out fast. 

While power consumption is a not a constraint with the downlink, hence it enjoys ofdm ! 

high PAPR results in higher power consumption.

Is this the only issue? I have read that high PAPR will also result in sub-carrier interference. Is this correct?

Not sure about sub carrier interference but due to PAPR there is also inter modulation(IP3) which will distort the transmitted constellation. 

thank you very much