Spells only do what they say they do.
The spell description of SpritSpirit Shroud states:
Until the spell ends, any attack you make deals 1d8 extra damage when you hit a creature within 10 feet of you. This damage is radiant, necrotic, or cold (your choice when you cast the spell). Any creature that takes this damage can’t regain hit points until the start of your next turn.
Nothing in the description of the spell references healing undead. So unless your DM decides otherwise, it won't heal them.
As far as I know, the positive/negative energy mechanics were scrapped in 5e, compared to previous editions. Any healing side effect on undead is always written in the spell's description if relevant (for example, see the spell Negative Energy Flood, from Xanathar's Guide To Everything).
In the end, your DM makes the rules
As Doppelgreener mentioned, it would seem like your DM has set up some homebrew rules to emulate positive/negative energy interactions with undead, probably inspired by previous editions. Since nothing of the sort seems to exist in the 5e official rules, it's up to them to rule whether some spells can or cannot heal undead.