You have to plan the steps of the budding romance into your story, either before you write the first draft, or at the editing stage.
For planning purposes, treat the romance as a story in it’s own right, with it’s own romance story arc: boy meets girl, boy loses girl, boy and girl reconcile, girl loses boy, both reconcile and compromise, etc. This may be a totally different shape arc to your main story. However, this is basically a story of one genre within the story of another genre.
Your love story may not be your main story, but you still need to plan out how that story porogresses and what are the main scene. Then you need to weave those scenes or scenes snippets into the scenes of your main story. Also, maybe adding additional scenes if they are key to the love story alone.
Writing in the first person has its own skill sets and requires stylistic discipline:
Watch out for tense drift. It is incredibly easy to slip from first person present tense to first person past tense and vica-versa. Even within the same paragraph or sentence. Decide which tense you are writing in, and stick to it scrupulously.
Always start a new paragraph for each new character, regardless of whether they are speaking or taking action. This is especially key if, like yourself, you are using minimal idetifyers (he said, she said etc). This clarifies exactly who is doing what and when. Yes, this means some of your paragraphs will be really short, but clariry must be the priority. Could this also be a sign you need more description?
Once the first draft is completed, I always dedicate an entire round of editing just to pick up these first-person issues.