I recently injured my hamstrings and feel really tight. What can I do to increase my hip mobility?

Hamstring, and other muscle/tendon, issues can take a long time to heal. The key is providing the appropriate load (usually done via eccentric strengthening) to promote tissue remodeling and increase resiliency of the tissue so you avoid future injury. It is also important to look at the kinetic chain of motion - low back, pelvis, hips, knee, ankle, etc. and what the demands of your activities are. There are many hip joint stretches, mobility exercises, and self joint mobilization strategies that can be done with improve hip mobility. It's important to assess what needs to be improved and make a plan of attack based on your specific movement patterns and needs.

First off, if you're past the acute stage, get back to normal use. Depending on how severe the injury is, it can vary in how long you'll take to "feel" back to normal. Give your body the variety of movement it wants. A broad movement practice is important for anybody, and even more important to those with limited range of motion. Moving in novel ways helps your nervous system map itself and gives you a greater capacity for "safety" when you get into strange positions. Getting some bodywork could also be helpful to your body's natural course of action in healing itself.