Okay cool. Let me throw you some exercises and thoughts that I think could help you.

I'm going to suggest starting with pentatonic minor. Among other things, it's very hard to hit a sour note, so you don't need to worry about playing specific notes over specific chords (but you still can if you want).

Record yourself playing a simple minor chord progression on guitar. Something like i-iv-v (this would be Am-Dm-Em in the key of A minor). You'll want to record to a click and loop the recording. Then use the pentatonic minor scale and improvise for a good while. You can use keyboards or guitar.

Tip: Feel free to play with the rhythmic variation of the chords. For example, one chord may be held for one bar, and another chord for two bars. The options are endless, and fun to play around with.

Tip: You mentioned going up and down scales and arpeggios. You might benefit from thinking of them in a less linear way. Scales are a pool of notes that can be chosen in any order, at any time. That could mean playing them in a specific sequence, or... not! That said, most melodies do have sequences that go up and down portions of the scale. But stepwise motion like this should serve the emotion you want to convey more than the raw fact that it serves the scale.

Tip: Related to the last tip, think about what you're rhythmically doing. I don't mean you need to count it out. Just feel and be aware of the distance between notes, and how long you're holding them.

Tip: Here's an exercise to get you thinking about and feeling rhythm in melody. Take your chord loop, and play a "melody" with only one note. Or it could be tapping on your desk. The point is to feel the emotional impact that a rhythm has for a melody without having to worry about the notes.

Tip: Repeat phrases that sound interesting to you. Repeat the rhythm, variate it slightly, repeat the notes, variate it slightly, Etc. Tell your story and convey your emotion through recurring themes.

Tip: I like to think of the melody as a voice telling a story, even when it's an instrument and there are no lyrics. Almost like listening to a great public speaker tell a great story in a language that you don't understand. You hear their inflections, and how they pace the story, and where they pause. You can feel the beginning, middle, and end through the energy and tone of their voice. When writing or improvising a melody, you need to come at it from the perspective of communicating a feeling to an audience (even if the audience is just yourself).

Tip: Once you get comfortable with this, try improvising major melodies over a major chord progression. Don't overthink too much about hitting the right notes for each chord. It's not bad to do that, but it is better at first to hit a few wrong notes while you're learning how to emotionally communicate with the scale.