pic says it all, can't tell if the small round black things on lower leaf are bugs or eggs? Hosed it off with water until I can tell what I'm dealing with, should I use soap or oil or ??
The "round, black things " are the frass (poop) of the leaf tier caterpillar, a very common pest of Tecoma. Oil applications will be useless and probably the insecticidal soap, too. The caterpillars come out to feed but roll themselves up in a protective little fold of the leaves. If you look, you'll find them. I think I see a potential hideout in your picture.
Look for rolled leaves and squish them to dispatch the small caterpillar inside.
Thanks, I did indeed find 1/4" long tiny green caterpillars rolled up in some of the leaves.
Ta da! :-) Now that you know what to look for, you can squish away.