Sentiment analysis in natural language processing (NLP), endeavors to computationally identify and extract subjective information from textual data. In code-mixed text, sentiment analysis presents a unique challenge due to the mixing of languages within a single textual context. For low-resourced languages such as Tamil and Tulu, predicting sentiment becomes a challenging task due to the presence of text comprising various scripts. In this research, we present the sentiment analysis of code-mixed Tamil and Tulu Youtube comments. We have developed a Bidirectional Long-Short Term Memory (BiLSTM) networks based models for both languages which further uses contextualized word embeddings at input layers of the models. For that purpose, ELMo embeddings have been trained on larger unannotated code-mixed text like corpora. Our models performed with macro average F1-scores of 0.2877 and 0.5133 on Tamil and Tulu code-mixed datasets respectively.