Is it allowed?
for example, a trip to a mall for a day?
Buying clothing is problematic. Other things are OK unless there’s a big Simcha. (sorry - a little late for this year)
Can we get a little more specifc here? 3 weeks vs 9 days? would buying a new suit/dress only be assur? buying polo shirts/shabbos shirts ok if needed? (even if not needed maybe). going to a store vs. tapping buttons on amazon for a delivery of some shirts?
Sure!
This mostly applies in the 9 days for Ashkenazim and Week of T"B for Sephardim.
No difference between in a store vs ordering online.
Additionally, there’s a custom not to buy things that would require a shehecheyanu (like a new suit) during the entire 3 weeks (SA 551:17).