Hotend is oozing out the sides and getting in the way of my print
Looking at the picture of your nozzle, it appears to seal against the heat break and not the Bowden tube.  (A nozzle sealing against the heat break will have an entry hole of about 2 mm dia. for 1.75 mm filament.  A nozzle will have an opening large enough for the Bowden tube to slip into if it seals against the Bowden tube.)
If your heat break is all metal, you have an all metal hot end that can extrude above 250 °C.  If your heat break has a Teflon tube inside it, your hot has a highest temperature below 250 °C to avoid degrading the Teflon.  Both follow the same procedure below, but you highest temperature for making the seal will be different.
To see if your nozzle is OK (not clogged), try pulling the filament out with the hot end at temperature (same procedure as unloading filament).  Trim the irregularities off the filament while leaving a sharp end.  Then, see if you can push the filament through the nozzle at extrusion temperature.
If still clogged, remove the nozzle (you will need to tighten it later anyway) and see if the filament will go through without the nozzle.
After camera piture: unless your hot end is all metal, the Bowden tube likely forms the seal to the nozzle.  See if the length of the tube going into the hotend goes down to the nozzle.  The end of the tube needs to be smooth to make the seal and the seal surface to the nozzle needs to be clean or the filament material soft enough to push out of the way.  Pull up to release the tube.  When you push down to lock the tube in, it should push the tube against the nozzle.
For an all metal hot end follow the procedure below.
Before camera picture:
Sounds like you lost the seal between the nozzle and the heat break.  For most hotends (unless you have a plastic tube that pushes up against the nozzle) heat up to the maximum hotend temperature, then tighten the nozzle tight against the heat break in the heat block, to form a seal between the two.
If the nozzle tightens against the heat block before the heat break, you won't get a seal.  You should see some threads of the nozzle exposed and not in the heat block.
Take care not to over tighten the heat break in the heat sink because the heat break is thin going into the heat sink to minimize heat conduction and will easily break.
If your seal to the nozzle is with a plastic tube, investigate why you don't have a seal.
Looking at picture:
Follow the above procedure while the heat break to the heat sink is of less consern since it appears that separate screws tighten it into the heat sink.