The recent outbreak of COVID-19 has brought the entire world to a standstill. The rapid pace at which the virus has spread across the world is unprecedented. The sheer number of infected cases and fatalities in such a short period of time has overwhelmed medical facilities across the globe. The rapid pace of the spread of the novel coronavirus makes it imperative that its' spread be forecasted well in advance in order to plan for eventualities. An accurate early forecasting of the number of cases would certainly assist governments and various other organizations to strategize and prepare for the newly infected cases, well in advance. In this work, a novel method of forecasting the future cases of infection, based on the study of data mined from the internet search terms of people in the affected region, is proposed. The study utilizes relevant Google Trends of specific search terms related to COVID-19 pandemic along with European Centre for Disease prevention and Control (ECDC) data on COVID-19 spread, to forecast the future trends of daily new cases, cumulative cases and deaths for India, USA and UK. For this purpose, a hybrid GWO-LSTM model is developed, where the network parameters of Long Short Term Memory (LSTM) network are optimized using Grey Wolf Optimizer (GWO). The results of the proposed model are compared with the baseline models including Auto Regressive Integrated Moving Average (ARIMA), and it is observed that the proposed model achieves much better results in forecasting the future trends of the spread of infection. Using the proposed hybrid GWO-LSTM model incorporating online big data from Google Trends, a reduction in Mean Absolute Percentage Error (MAPE) values for forecasting results to the extent of about 98% have been observed. Further, reduction in MAPE by 74% for models incorporating Google Trends was observed, thus, confirming the efficacy of utilizing public sentiments in terms of search frequencies of relevant terms online, in forecasting pandemic numbers.