Let me jump in here, and speak based on my experience with BCG.
Top tier consulting firms typically evaluate the following in order to invite a candidate for an interview:
1. University brand name (e.g. ~top 5-10 universities in the country)
2. University grades (e.g. minimum 3.70/4.00 GPA)
3. Relevant professional experience (e.g. internships, volunteering)
4. Extra-curricular activies (e.g. positions held in university societies)
1 and 2 are typically the hygiene factors i.e. one should graduate from a reputable university with decent grades. It seems that you are already meeting both criteria. Please note that it is uncommon that a candidate from the same school with 3.90 GPA would be prioritized before you purely based on the grades.
3 and 4 are the real differentiators. Thereby, you would need to highlight the relevance of your internship and extracurricular, and how these will help you in your work as a consultant.
Best of luck!