I know this is awkward and I did not find any answers to my question, but I want to ask, is it ok to apply sunscreen on my lady parts (vaginal area)?

Depends. Sunscreens are to be used for skin only. But, if you intend to use them on mucous membranes, do a small test area first to be sure there is no burning, stinging, allergies, or other side effects. Be aware that potential systemic absorption may be toxic.
Usually . Some sunblocks may cause a burning sensation when they come in contact with mucous membranes. Zinc oxide products typically do not. Otherwise it would be a good idea if you are sunbathing in the nude.