Nothing to be embarrassed about. This matchup is more complicated than a lot of people let on imo. Peach has a lot of tricks that you want to identify and exploit.
First, try to figure out what is hurting you, dash attack/dsmash or turnips/float approaches?
Personally I find dash attack and dsmash much more threatening, so I try to focus on not getting hit by those. However, if you can bait these moves you can get grabs and big punishes, so the best thing to do is DD or just walk up approach peach cautiously with her dash attacks misleading range in mind. Don't commit to anything too soon and understand that marth's range and capability to punish peach hard puts a lot of the pressure on peach to "do something," which you can then take advantage of. Watch out for peach rolling into you and dsmashing. Peaches love to do that.
For turnip approaches, there are a bunch of tricks to avoid them. If you see her pull a turnip, and you anticipate her jump, throw, float, aerial approach, you can do many things. Dash underneath her and cross her up, then reverse fsmash her. You can use nair's double hits to 1st deflect the turnip and 2nd to hit peach, which should also start a nice combo for you. If you have enough space behind you you can just retreat past the turnip's range with retreat fair and keep peach out. You can also counter turnip approaches, but be careful not to overuse this as she can punish you badly if she predicts it.
I seriously don't recommend shielding very much against her aerials. Peach's shield pressure is fantastic, and particularly you need to understand that bair -> dsmash is not shieldable (it will erode your shield enough to the point that the later hits of dsmash will connect).
As far as killing goes, this is the really challenging part of the matchup. You don't have a reliable way to kill her. Have you tried side B -> up tilt? That works sometimes, but not for long. Peaches CC constantly and I'm pretty tentative to try to challenge peach's air game with side B, plus they can DI out of it if they're ready for it. It's the kind of thing to keep up your sleeve. It might work every once in a while, but you certainly can't rely on it.
Another "gimp" on peach is to fthrow her near the ledge straight into a full hop dair. If you catch the peach DIing your fthrow in (try to fthrow instantly after grab, it scares even really good people into DIing in sometimes) you can take advantage of this with either fsmash or full hop dair. Full hop dair won't kill at very low percents, but there is a large overlap in % where fsmashing is not going to kill and dair will.
You mentioned air dodges --- bait air dodges! Watch peach hover and just be patient. Try to keep in mind that you are marth and you are scary, so peach is very likely to commit to some type of move (air dodge, aerial attack) before marth does in order to protect herself. Wait for the air dodge and fsmash/grab/up tilt. If you can force her to up B, lots of peaches like to go for the ledge from the umbrella. Don't dtilt...it won't work...just try to take the ledge quickly and roll up right before they get there, then you can ledge hop nair or something if they end up drifting on stage.
You just have to be really patient with peach. Sometimes she is going to live a really really long time and its going to seem like you will never kill her. Just stay focused and keep hitting her, keep baiting air dodges, and eventually she will die.
